Thread: "Social dream"

From: "Eduard" <baumann@mcnet.ch>
Date: Sat, 19 Feb 2011 14:13:54 -0000
Subject: Social dream



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(a) Introduction



The marvelaous 120-Cell in 4D.



The 4D Regulars are very sympathic models of perfect democratic
societies with perfectly equal individuals. Each has an equal number of
neighbours in equal constellation. This number is 4 for the 5-Cell, 6
for the hypercube (8 `individuals') and 12 for the 120-Cell (120
`individuals' =3D society).

A cluster of bees in winter has to arrange changes of roles (inner /
outer places in the cluster). Everybody wants be in the warmer inner
space. No such problems in 4D at least for 120 bees housed in the
120-Cell. Everybody is equally surrounded by 12 neighbours. Perhaps
arrange the bees in 3D in a infinite grid to avoid social problems.



Let me use the abreviations =84Magic" for the program Magic120Cell
and =84Hyper" for the Hypermeaminx puzzle in MC4D.



(b) Combine Magic and Hyper.



I think Magic and Hyper cannot share their log files.

Complementarity: Magic has finding help and no macro, Hyper has no
finding help but macro.

I need both!

How about a transfer program?

Roice: can you give me a table with the two corresponding labelings of
stickers in Magic and Hyper? I need also to know the signification of
the last digit of the numbers in Magic log file (2 clockwise and 4
anticlockwise for faces, what is 6 and 8?).



(c) Partial HOF



The HOF for the 120-Cell has only two entries until now. Noel Chalmers
and Matt Galla (great performer). In order to achive more participants
(about 400 as in the Al Zimmerman contests) I propose to install HOF for
partial results.

For this I need an evaluator, a program which calculates the percentage
of cubies in place and well oriented from the log file. The code must
already existe for the checking and emitting "Congratulations"
in MC4D.

With this evaluator a ranking list is possible as in the Al Zimmerman
contests (take best results of each participant).

This can be a good motivation to get in touch with the 120-Cell and live
a moment in the world of this 120 individuals (dodecahedra).



If I get the evaluator and the incoming log files

I propose to do the managing this of partial HOF in
superliminal.com/wiki (in protected pages).



Doing only the 2 colored faces in the 120-Cell is already demanding
because you have to get a good feeling of the neighbourhoods and soon to
use commutators to avoid the disturbing of already placed cubies.



If this partial HOF is working I propose to do promotion in (1)
Roice's description of Magic120Cell, (2) Roice's description of
MC4D, (3) Superliminal.com/wiki and (4) in the "4D cubing"
forum.


What do you think all?

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=
(a) Introduction


=
 


lang=3D"EN-GB">The marvelaous 120-Cell in 4D.


lang=3D"EN-GB"> 


lang=3D"EN-GB">The 4D Regulars are very sympathic models of perfect democra=
tic societies with perfectly equal individuals. Each has an equal number of=
neighbours in equal constellation. This number is 4 for the 5-Cell, 6 for =
the hypercube (8 `individuals') and 12 for the 120-Cell (120 `individuals' =
=3D society).


lang=3D"EN-GB">A cluster of bees in winter has to arrange changes of roles =
(inner / outer places in the cluster). Everybody wants be in the warmer inn=
er space. No such problems in 4D at least for 120 bees housed in the 120-Ce=
ll. Everybody is equally surrounded by 12 neighbours. Perhaps arrange the b=
ees in 3D in a infinite grid to avoid social problems.


lang=3D"EN-GB"> 


lang=3D"EN-GB">Let me use the abreviations =84Magic" for the program Magic1=
20Cell and =84Hyper" for the Hypermeaminx puzzle in MC4D.


lang=3D"EN-GB"> 


lang=3D"EN-GB">(b) Combine Magic and Hyper.


lang=3D"EN-GB"> 


lang=3D"EN-GB">I think Magic and Hyper cannot share their log files.=


lang=3D"EN-GB">Complementarity: Magic has finding help and no macro, Hyper =
has no finding help but macro.


lang=3D"EN-GB">I need both!


lang=3D"EN-GB">How about a transfer program?


Roice: c=
an you give me a table with the two corresponding labelings of stickers in =
Magic and Hyper? I need also to know the signification of the last digit of=
the numbers in Magic log file (2 clockwise and 4 anticlockwise for faces, =
what is 6 and 8?).


 >


(c) Part=
ial HOF


 >


lang=3D"EN-GB">The HOF for the 120-Cell has only two entries until now. Noe=
l Chalmers and Matt Galla (great performer). In order to achive more partic=
ipants (about 400 as in the Al Zimmerman contests) I propose to install HOF=
for partial results.


lang=3D"EN-GB">For this I need an evaluator, a program which calcula=
tes the percentage of cubies in place and well oriented from the log file. =
The code must already existe for the checking and emitting "Congratulations=
" in MC4D.


lang=3D"EN-GB">With this evaluator a ranking list is possible as in the Al =
Zimmerman contests (take best results of each participant).
P>

lang=3D"EN-GB">This can be a good motivation to get in touch with the 120-C=
ell and live a moment in the world of this 120 individuals (dodecahedra).>


lang=3D"EN-GB"> 


lang=3D"EN-GB">If I get the evaluator and the incoming log filesAN>


lang=3D"EN-GB">I propose to do the managing this of partial HOF in superlim=
inal.com/wiki (in protected pages).


lang=3D"EN-GB"> 


lang=3D"EN-GB">Doing only the 2 colored faces in the 120-Cell is already de=
manding because you have to get a good feeling of the neighbourhoods and so=
on to use commutators to avoid the disturbing of already placed cubies.<=
/o>


lang=3D"EN-GB"> 


lang=3D"EN-GB">If this partial HOF is working I propose to do promotion in =
(1) Roice's description of Magic120Cell, (2) Roice's description of MC4D, (=
3) Superliminal.com/wiki and (4) in the "4D cubing" forum.
=3D"EN-GB">


lang=3D"EN-GB"> 

NT-SIZE: 10pt;" lang=3D"EN-GB">What do you think all?

--5-1590343889-5246059429=:4--




From: Roice Nelson <roice3@gmail.com>
Date: Sun, 20 Feb 2011 12:54:49 -0600
Subject: Re: [MC4D] Social dream



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Hi Eduard,

I can't give you the "table of stickers" you are asking for, because it
would be huge. I can briefly describe the log file encoding though. In
Magic120Cell, all the information for a twist is encoded into a 32-bit
integer, which is what you see in the log files. There are 63 stickers per
cell, so 6 bits are required for that. 7 bits are needed to record which o=
f
the 120 cells the sticker is on. 1 bit is used to record the twist
direction, and another for whether or not it is a view rotation. In
retrospect, I don't like that I packed it all into an integer. It is
compact, but people want to look in the log files and understand them, and
this representation is opaque. For the MagicTile log files I did a few
weeks ago, I made it more reader friendly. Andrey has suggested we come up
with a standard format, so I'm sure some of these issues will arise when
that is discussed.

MC4D has a different encoding of twists. I didn't check the source code
(which is available
online),
but I'm pretty sure the last digit you were asking about is a
bitmaskrepresenting the
slicemask of the twist (which slices were held down while
twisting). For the 120-cell puzzle with 3 stickers-per-side, this is not a=
n
import piece of information, which is why it wasn't part of my twist
definition above. But for other MC4D puzzles, it is important. If you had
a 120-cell puzzle with 5 stickers per side, slicemask would need to be
included.

Here are my other thoughts on this.

- I like the competitions and think they are good motivators, so making it
such that more could participate is a worthy and positive goal. (As an
aside, I think it'd be cool if this could be more automated...that is, if
the software could directly support logging solutions online without human
intervention.)
- While effort could be expended on a log file transfer program, I think
the better long term solution here would be to add the missing features to
MC4D and retire the Magic120Cell code. Also, I think the log file
standardization Andrey has suggested would sidestep this need, assuming the
various implementations were updated to respect it.
- An "evaluator" feature could be added directly to MC4D, which would show
the percentage completed on the puzzle. You could calculate percentage
complete on either a sticker or piece basis. This feature request would be
good to add to the issue
tracker,
so that it will be ready for when someone is motivated to work on it. I do
know it will be a difficult problem to handle generally in MC4D, due to
even-length puzzles where there aren't unmoving central stickers. I ran
into this when adding this feature to MC5D. FYI, right now, the MC4D code
just cycles through stickers on a face and checks whether they are all the
same, and does this for each face. Once it finds one different, it knows i=
t
is not solved and immediately returns. So it doesn't need to think about
how much of the puzzle is completed.

Best,
Roice


On Sat, Feb 19, 2011 at 8:13 AM, Eduard wrote:

>
>
> (a) Introduction
>
>
>
> The marvelaous 120-Cell in 4D.
>
>
>
> The 4D Regulars are very sympathic models of perfect democratic societies
> with perfectly equal individuals. Each has an equal number of neighbours =
in
> equal constellation. This number is 4 for the 5-Cell, 6 for the hypercube=
(8
> `individuals') and 12 for the 120-Cell (120 `individuals' =3D society).
>
> A cluster of bees in winter has to arrange changes of roles (inner / oute=
r
> places in the cluster). Everybody wants be in the warmer inner space. No
> such problems in 4D at least for 120 bees housed in the 120-Cell. Everybo=
dy
> is equally surrounded by 12 neighbours. Perhaps arrange the bees in 3D in=
a
> infinite grid to avoid social problems.
>
>
>
> Let me use the abreviations =84Magic" for the program Magic120Cell and
> =84Hyper" for the Hypermeaminx puzzle in MC4D.
>
>
>
> (b) Combine Magic and Hyper.
>
>
>
> I think Magic and Hyper cannot share their log files.
>
> Complementarity: Magic has finding help and no macro, Hyper has no findin=
g
> help but macro.
>
> I need both!
>
> How about a *transfer* program?
>
> Roice: can you give me a table with the two corresponding labelings of
> stickers in Magic and Hyper? I need also to know the signification of the
> last digit of the numbers in Magic log file (2 clockwise and 4 anticlockw=
ise
> for faces, what is 6 and 8?).
>
>
>
> (c) Partial HOF
>
>
>
> The HOF for the 120-Cell has only two entries until now. Noel Chalmers an=
d
> Matt Galla (great performer). In order to achive more participants (about
> 400 as in the Al Zimmerman contests) I propose to install HOF for partial
> results.
>
> For this I need an *evaluator*, a program which calculates the percentage
> of cubies in place and well oriented from the log file. The code must
> already existe for the checking and emitting "Congratulations" in MC4D.
>
> With this evaluator a ranking list is possible as in the Al Zimmerman
> contests (take best results of each participant).
>
> This can be a good motivation to get in touch with the 120-Cell and live =
a
> moment in the world of this 120 individuals (dodecahedra).
>
>
>
> If I get the evaluator and the incoming log files
>
> I propose to do the managing this of partial HOF in superliminal.com/wiki=
(in protected pages).
>
>
>
> Doing only the 2 colored faces in the 120-Cell is already demanding becau=
se
> you have to get a good feeling of the neighbourhoods and soon to use
> commutators to avoid the disturbing of already placed cubies.
>
>
>
> If this partial HOF is working I propose to do promotion in (1) Roice's
> description of Magic120Cell, (2) Roice's description of MC4D, (3)
> Superliminal.com/wiki and (4) in the "4D cubing" forum.
>
>
> What do you think all?
>
>

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Hi Eduard,


I can't give you the "table of stick=
ers" you are asking for, because it would be huge. =A0I can briefly de=
scribe the log file encoding though. =A0In Magic120Cell, all the informatio=
n for a twist is encoded into a 32-bit integer, which is what you see in th=
e log files. =A0There are 63 stickers per cell, so 6 bits are required for =
that. =A07 bits are needed to record which of the 120 cells the sticker is =
on. =A01 bit is used to record the twist direction, and another for whether=
or not it is a view rotation. =A0In retrospect, I don't like that I pa=
cked it all into an integer. =A0It is compact, but people want to look in t=
he log files and understand them, and this representation is opaque. =A0For=
the MagicTile log files I did a few weeks ago, I made it more reader frien=
dly. =A0Andrey has suggested we come up with a standard format, so I'm =
sure some of these issues will arise when that is discussed.



MC4D has a different encoding of twists. =A0I didn'=
t check the source code (which is cube4d/source/browse/" target=3D"_blank">available online), but I'm=
pretty sure the last digit you were asking about is a .wikipedia.org/wiki/Bitmask" target=3D"_blank">bitmask representing the=
slicemask of the twist (which slices were held down while twisting). =A0Fo=
r the 120-cell puzzle with 3 stickers-per-side, this is not an import piece=
of information, which is why it wasn't part of my twist definition abo=
ve. =A0But for other MC4D puzzles, it is important. =A0If you had a 120-cel=
l puzzle with 5 stickers per side, slicemask would need to be included.v>


Here are my other thoughts on this. =A0

<=
/div>
- =A0I like the competitions and think they are good motivators, =
so making it such that more could participate is a worthy and positive goal=
. =A0(As an aside, I think it'd be cool if this could be more automated=
...that is, if the software could directly support logging solutions online=
without human intervention.)


- =A0While effort could be expended on a log file transfer program, I =
think the better long term solution here would be to add the missing featur=
es to MC4D and retire the Magic120Cell code. =A0Also, I think the log file =
standardization Andrey has suggested would sidestep this need, assuming the=
various implementations were updated to respect it.


- =A0An "evaluator" feature could be added directly to MC4D,=
which would show the percentage completed on the puzzle. =A0You could calc=
ulate percentage complete on either a sticker or piece basis. =A0This=A0fea=
ture request would be good to add to the p/magiccube4d/issues/list" target=3D"_blank">issue tracker, so that it =
will be ready for when someone is motivated to work on it. =A0I do know it =
will be a difficult problem to handle generally in MC4D, due to even-length=
puzzles where there aren't unmoving central stickers. =A0I ran into th=
is when adding this feature to MC5D. =A0FYI, right now, the MC4D code just =
cycles through stickers on a face and checks whether they are all the same,=
and does this for each face. =A0Once it finds one different, it knows it i=
s not solved and immediately returns. =A0So it doesn't need to think ab=
out how much of the puzzle is completed.



Best,
Roice


=3D"gmail_quote">On Sat, Feb 19, 2011 at 8:13 AM, Eduard =
<baumann@mcnet.ch<=
/a>>
wrote:


x #ccc solid;padding-left:1ex">






=20=20=20=20=20=20=20=20

















(a)=
Introduction


=A0=


g=3D"EN-GB">The marvelaous 120-Cell in 4D.


g=3D"EN-GB">=A0


g=3D"EN-GB">The 4D Regulars are very sympathic models of perfect democratic=
societies with perfectly equal individuals. Each has an equal number of ne=
ighbours in equal constellation. This number is 4 for the 5-Cell, 6 for the=
hypercube (8 `individuals') and 12 for the 120-Cell (120 `individuals&=
#39; =3D society).




g=3D"EN-GB">A cluster of bees in winter has to arrange changes of roles (in=
ner / outer places in the cluster). Everybody wants be in the warmer inner =
space. No such problems in 4D at least for 120 bees housed in the 120-Cell.=
Everybody is equally surrounded by 12 neighbours. Perhaps arrange the bees=
in 3D in a infinite grid to avoid social problems.




g=3D"EN-GB">=A0


g=3D"EN-GB">Let me use the abreviations =84Magic" for the program Magi=
c120Cell and =84Hyper" for the Hypermeaminx puzzle in MC4D.


g=3D"EN-GB">=A0


g=3D"EN-GB">(b) Combine Magic and Hyper.


g=3D"EN-GB">=A0


g=3D"EN-GB">I think Magic and Hyper cannot share their log files.>

g=3D"EN-GB">Complementarity: Magic has finding help and no macro, Hyper has=
no finding help but macro.


g=3D"EN-GB">I need both!


g=3D"EN-GB">How about a transfer program?


Roice: can you give me a table=
with the two corresponding labelings of stickers in Magic and Hyper? I nee=
d also to know the signification of the last digit of the numbers in Magic =
log file (2 clockwise and 4 anticlockwise for faces, what is 6 and 8?).nt>




=A0


(c) Partial HOF<=
/p>

=A0


g=3D"EN-GB">The HOF for the 120-Cell has only two entries until now. Noel C=
halmers and Matt Galla (great performer). In order to achive more participa=
nts (about 400 as in the Al Zimmerman contests) I propose to install HOF fo=
r partial results.




g=3D"EN-GB">For this I need an evaluator, a program which calculates=
the percentage of cubies in place and well oriented from the log file. The=
code must already existe for the checking and emitting "Congratulatio=
ns" in MC4D.




g=3D"EN-GB">With this evaluator a ranking list is possible as in the Al Zim=
merman contests (take best results of each participant).


g=3D"EN-GB">This can be a good motivation to get in touch with the 120-Cell=
and live a moment in the world of this 120 individuals (dodecahedra).n>




g=3D"EN-GB">=A0


g=3D"EN-GB">If I get the evaluator and the incoming log files


g=3D"EN-GB">I propose to do the managing this of partial HOF in http://superliminal.com/wiki" target=3D"_blank">superliminal.com/wiki (=
in protected pages).




g=3D"EN-GB">=A0


g=3D"EN-GB">Doing only the 2 colored faces in the 120-Cell is already deman=
ding because you have to get a good feeling of the neighbourhoods and soon =
to use commutators to avoid the disturbing of already placed cubies.
=




g=3D"EN-GB">=A0


g=3D"EN-GB">If this partial HOF is working I propose to do promotion in (1)=
Roice's description of Magic120Cell, (2) Roice's description of MC=
4D, (3) Superliminal.com/wiki and (4) in the "4D cubing" forum.span>




g=3D"EN-GB">=A0

lang=3D"EN-GB">What do you think all?









=20=20=20=20
=20=20=20=20






=



--0015174c1c2820512d049cbb48cb--




From: "Eduard" <baumann@mcnet.ch>
Date: Sun, 20 Feb 2011 22:26:30 -0000
Subject: Re: [MC4D] Social dream






Hi Roice, thanks very much for the answer.

I see both the transfer program and the evaluator need work..
I prefer the piece-evaluator (stickers can be in place without any worth).
I see an evaluator problem for not layered methods as that in the RubikExpl=
orer for 3D.

The sticker-label-table for transfer is only about 7000 lines long.
Unpack the integer values is not a problem for me, but what about the numbe=
ring sequence. Is the numbering sequence in "Magic120Cell" and in MC4D topo=
logically equivalent or are they both arbitrary and it is very difficult to=
associate the two numberings?

I'm interested to start NOW with the faces in Magic120Cell where no macros =
are needed and the find option is very usefull. This will cost lot of hours=
(weeks). I'm sure that I will not want to continue without macros (edges a=
nd corners). In this case the transfer is very important for me.


--- In 4D_Cubing@yahoogroups.com, Roice Nelson wrote:
>
> Hi Eduard,
>=20
> I can't give you the "table of stickers" you are asking for, because it
> would be huge. I can briefly describe the log file encoding though. In
> Magic120Cell, all the information for a twist is encoded into a 32-bit
> integer, which is what you see in the log files. There are 63 stickers p=
er
> cell, so 6 bits are required for that. 7 bits are needed to record which=
of
> the 120 cells the sticker is on. 1 bit is used to record the twist
> direction, and another for whether or not it is a view rotation. In
> retrospect, I don't like that I packed it all into an integer. It is
> compact, but people want to look in the log files and understand them, an=
d
> this representation is opaque. For the MagicTile log files I did a few
> weeks ago, I made it more reader friendly. Andrey has suggested we come =
up
> with a standard format, so I'm sure some of these issues will arise when
> that is discussed.
>=20
> MC4D has a different encoding of twists. I didn't check the source code
> (which is available
> online),
> but I'm pretty sure the last digit you were asking about is a
> bitmaskrepresenting the
> slicemask of the twist (which slices were held down while
> twisting). For the 120-cell puzzle with 3 stickers-per-side, this is not=
an
> import piece of information, which is why it wasn't part of my twist
> definition above. But for other MC4D puzzles, it is important. If you h=
ad
> a 120-cell puzzle with 5 stickers per side, slicemask would need to be
> included.
>=20
> Here are my other thoughts on this.
>=20
> - I like the competitions and think they are good motivators, so making =
it
> such that more could participate is a worthy and positive goal. (As an
> aside, I think it'd be cool if this could be more automated...that is, if
> the software could directly support logging solutions online without huma=
n
> intervention.)
> - While effort could be expended on a log file transfer program, I think
> the better long term solution here would be to add the missing features t=
o
> MC4D and retire the Magic120Cell code. Also, I think the log file
> standardization Andrey has suggested would sidestep this need, assuming t=
he
> various implementations were updated to respect it.
> - An "evaluator" feature could be added directly to MC4D, which would sh=
ow
> the percentage completed on the puzzle. You could calculate percentage
> complete on either a sticker or piece basis. This feature request would =
be
> good to add to the issue
> tracker,
> so that it will be ready for when someone is motivated to work on it. I =
do
> know it will be a difficult problem to handle generally in MC4D, due to
> even-length puzzles where there aren't unmoving central stickers. I ran
> into this when adding this feature to MC5D. FYI, right now, the MC4D cod=
e
> just cycles through stickers on a face and checks whether they are all th=
e
> same, and does this for each face. Once it finds one different, it knows=
it
> is not solved and immediately returns. So it doesn't need to think about
> how much of the puzzle is completed.
>=20
> Best,
> Roice
>=20
>=20
> On Sat, Feb 19, 2011 at 8:13 AM, Eduard wrote:
>=20
> >
> > (a) Introduction
> >
> > The marvelaous 120-Cell in 4D.
> >
> > The 4D Regulars are very sympathic models of perfect democratic societi=
es
> > with perfectly equal individuals. Each has an equal number of neighbour=
s in
> > equal constellation. This number is 4 for the 5-Cell, 6 for the hypercu=
be (8
> > `individuals') and 12 for the 120-Cell (120 `individuals' =3D society).
> >
> > A cluster of bees in winter has to arrange changes of roles (inner / ou=
ter
> > places in the cluster). Everybody wants be in the warmer inner space. N=
o
> > such problems in 4D at least for 120 bees housed in the 120-Cell. Every=
body
> > is equally surrounded by 12 neighbours. Perhaps arrange the bees in 3D =
in a
> > infinite grid to avoid social problems.
> >
> > Let me use the abreviations =84Magic" for the program Magic120Cell and
> > =84Hyper" for the Hypermeaminx puzzle in MC4D.
> >
> >
> > (b) Combine Magic and Hyper.
> >
> > I think Magic and Hyper cannot share their log files.
> >
> > Complementarity: Magic has finding help and no macro, Hyper has no find=
ing
> > help but macro.
> >
> > I need both!
> >
> > How about a *transfer* program?
> >
> > Roice: can you give me a table with the two corresponding labelings of
> > stickers in Magic and Hyper? I need also to know the signification of t=
he
> > last digit of the numbers in Magic log file (2 clockwise and 4 anticloc=
kwise
> > for faces, what is 6 and 8?).
> >
> >
> > (c) Partial HOF
> >
> > The HOF for the 120-Cell has only two entries until now. Noel Chalmers =
and
> > Matt Galla (great performer). In order to achive more participants (abo=
ut
> > 400 as in the Al Zimmerman contests) I propose to install HOF for parti=
al
> > results.
> >
> > For this I need an *evaluator*, a program which calculates the percenta=
ge
> > of cubies in place and well oriented from the log file. The code must
> > already existe for the checking and emitting "Congratulations" in MC4D.
> >
> > With this evaluator a ranking list is possible as in the Al Zimmerman
> > contests (take best results of each participant).
> >
> > This can be a good motivation to get in touch with the 120-Cell and liv=
e a
> > moment in the world of this 120 individuals (dodecahedra).
> >
> > If I get the evaluator and the incoming log files
> >
> > I propose to do the managing this of partial HOF in superliminal.com/wi=
ki(in protected pages).
> >
> > Doing only the 2 colored faces in the 120-Cell is already demanding bec=
ause
> > you have to get a good feeling of the neighbourhoods and soon to use
> > commutators to avoid the disturbing of already placed cubies.
> >
> > If this partial HOF is working I propose to do promotion in (1) Roice's
> > description of Magic120Cell, (2) Roice's description of MC4D, (3)
> > Superliminal.com/wiki and (4) in the "4D cubing" forum.
> >
> > What do you think all?
>




From: Roice Nelson <roice3@gmail.com>
Date: Sun, 20 Feb 2011 17:07:00 -0600
Subject: Re: [MC4D] Social dream



--0016e6da98b90002dd049cbece0e
Content-Type: text/plain; charset=windows-1252
Content-Transfer-Encoding: quoted-printable

Hi Eduard,

I'm sorry, but I do not think what you are asking for is trivial to do. Th=
e
sticker numbering sequence is indeed different among the two programs.
There is somewhat of a regular order in Magic120Cell (the first sticker of
each cell is the center, the next 12 are the 2C pieces, then 3C follow,
etc.), but this is not true in MC4D, where the stickers are created by a
generic polytope slicing engine that will not produce stickers in a
guaranteed, well-ordered manner. Furthermore, the cell ordering and cell
orientations certainly won't match, and this will also affect the sticker
numbering sequence.

In short, I'm afraid that without some complex custom coding, it will not b=
e
possible to generate the transfer table you'd like. So my apologies, but I
think you are out of luck until one of the developers has time to add a
piece finding feature to MC4D.

Take Care,
Roice


On Sun, Feb 20, 2011 at 4:26 PM, Eduard wrote:

>
>
>
> Hi Roice, thanks very much for the answer.
>
> I see both the transfer program and the evaluator need work..
> I prefer the piece-evaluator (stickers can be in place without any worth)=
.
> I see an evaluator problem for not layered methods as that in the
> RubikExplorer for 3D.
>
> The sticker-label-table for transfer is only about 7000 lines long.
> Unpack the integer values is not a problem for me, but what about the
> numbering sequence. Is the numbering sequence in "Magic120Cell" and in MC=
4D
> topologically equivalent or are they both arbitrary and it is very diffic=
ult
> to associate the two numberings?
>
> I'm interested to start NOW with the faces in Magic120Cell where no macro=
s
> are needed and the find option is very usefull. This will cost lot of hou=
rs
> (weeks). I'm sure that I will not want to continue without macros (edges =
and
> corners). In this case the transfer is very important for me.
>
>
> --- In 4D_Cubing@yahoogroups.com, Roice Nelson wrote:
> >
> > Hi Eduard,
> >
> > I can't give you the "table of stickers" you are asking for, because it
> > would be huge. I can briefly describe the log file encoding though. I=
n
> > Magic120Cell, all the information for a twist is encoded into a 32-bit
> > integer, which is what you see in the log files. There are 63 stickers
> per
> > cell, so 6 bits are required for that. 7 bits are needed to record whi=
ch
> of
> > the 120 cells the sticker is on. 1 bit is used to record the twist
> > direction, and another for whether or not it is a view rotation. In
> > retrospect, I don't like that I packed it all into an integer. It is
> > compact, but people want to look in the log files and understand them,
> and
> > this representation is opaque. For the MagicTile log files I did a few
> > weeks ago, I made it more reader friendly. Andrey has suggested we com=
e
> up
> > with a standard format, so I'm sure some of these issues will arise whe=
n
> > that is discussed.
> >
> > MC4D has a different encoding of twists. I didn't check the source cod=
e
> > (which is available
> > online),
> > but I'm pretty sure the last digit you were asking about is a
> > bitmaskrepresenting the
> > slicemask of the twist (which slices were held down while
> > twisting). For the 120-cell puzzle with 3 stickers-per-side, this is n=
ot
> an
> > import piece of information, which is why it wasn't part of my twist
> > definition above. But for other MC4D puzzles, it is important. If you
> had
> > a 120-cell puzzle with 5 stickers per side, slicemask would need to be
> > included.
> >
> > Here are my other thoughts on this.
> >
> > - I like the competitions and think they are good motivators, so makin=
g
> it
> > such that more could participate is a worthy and positive goal. (As an
> > aside, I think it'd be cool if this could be more automated...that is, =
if
> > the software could directly support logging solutions online without
> human
> > intervention.)
> > - While effort could be expended on a log file transfer program, I thi=
nk
> > the better long term solution here would be to add the missing features
> to
> > MC4D and retire the Magic120Cell code. Also, I think the log file
> > standardization Andrey has suggested would sidestep this need, assuming
> the
> > various implementations were updated to respect it.
> > - An "evaluator" feature could be added directly to MC4D, which would
> show
> > the percentage completed on the puzzle. You could calculate percentage
> > complete on either a sticker or piece basis. This feature request woul=
d
> be
> > good to add to the issue
> > tracker,
> > so that it will be ready for when someone is motivated to work on it. =
I
> do
> > know it will be a difficult problem to handle generally in MC4D, due to
> > even-length puzzles where there aren't unmoving central stickers. I ra=
n
> > into this when adding this feature to MC5D. FYI, right now, the MC4D
> code
> > just cycles through stickers on a face and checks whether they are all
> the
> > same, and does this for each face. Once it finds one different, it kno=
ws
> it
> > is not solved and immediately returns. So it doesn't need to think abo=
ut
> > how much of the puzzle is completed.
> >
> > Best,
> > Roice
> >
> >
> > On Sat, Feb 19, 2011 at 8:13 AM, Eduard wrote:
> >
> > >
> > > (a) Introduction
> > >
> > > The marvelaous 120-Cell in 4D.
> > >
> > > The 4D Regulars are very sympathic models of perfect democratic
> societies
> > > with perfectly equal individuals. Each has an equal number of
> neighbours in
> > > equal constellation. This number is 4 for the 5-Cell, 6 for the
> hypercube (8
> > > `individuals') and 12 for the 120-Cell (120 `individuals' =3D society=
).
> > >
> > > A cluster of bees in winter has to arrange changes of roles (inner /
> outer
> > > places in the cluster). Everybody wants be in the warmer inner space.
> No
> > > such problems in 4D at least for 120 bees housed in the 120-Cell.
> Everybody
> > > is equally surrounded by 12 neighbours. Perhaps arrange the bees in 3=
D
> in a
> > > infinite grid to avoid social problems.
> > >
> > > Let me use the abreviations =84Magic" for the program Magic120Cell an=
d
> > > =84Hyper" for the Hypermeaminx puzzle in MC4D.
> > >
> > >
> > > (b) Combine Magic and Hyper.
> > >
> > > I think Magic and Hyper cannot share their log files.
> > >
> > > Complementarity: Magic has finding help and no macro, Hyper has no
> finding
> > > help but macro.
> > >
> > > I need both!
> > >
> > > How about a *transfer* program?
> > >
> > > Roice: can you give me a table with the two corresponding labelings o=
f
> > > stickers in Magic and Hyper? I need also to know the signification of
> the
> > > last digit of the numbers in Magic log file (2 clockwise and 4
> anticlockwise
> > > for faces, what is 6 and 8?).
> > >
> > >
> > > (c) Partial HOF
> > >
> > > The HOF for the 120-Cell has only two entries until now. Noel Chalmer=
s
> and
> > > Matt Galla (great performer). In order to achive more participants
> (about
> > > 400 as in the Al Zimmerman contests) I propose to install HOF for
> partial
> > > results.
> > >
> > > For this I need an *evaluator*, a program which calculates the
> percentage
> > > of cubies in place and well oriented from the log file. The code must
> > > already existe for the checking and emitting "Congratulations" in MC4=
D.
> > >
> > > With this evaluator a ranking list is possible as in the Al Zimmerman
> > > contests (take best results of each participant).
> > >
> > > This can be a good motivation to get in touch with the 120-Cell and
> live a
> > > moment in the world of this 120 individuals (dodecahedra).
> > >
> > > If I get the evaluator and the incoming log files
> > >
> > > I propose to do the managing this of partial HOF in
> superliminal.com/wiki(in protected pages).
> > >
> > > Doing only the 2 colored faces in the 120-Cell is already demanding
> because
> > > you have to get a good feeling of the neighbourhoods and soon to use
> > > commutators to avoid the disturbing of already placed cubies.
> > >
> > > If this partial HOF is working I propose to do promotion in (1) Roice=
's
> > > description of Magic120Cell, (2) Roice's description of MC4D, (3)
> > > Superliminal.com/wiki and (4) in the "4D cubing" forum.
> > >
> > > What do you think all?
> >
>
>
>
>
> ------------------------------------
>
> Yahoo! Groups Links
>
>
>
>

--0016e6da98b90002dd049cbece0e
Content-Type: text/html; charset=windows-1252
Content-Transfer-Encoding: quoted-printable

Hi Eduard,


I'm sorry, but I do not think what you ar=
e asking for is trivial to do. =A0The sticker numbering sequence is indeed =
different among the two programs. =A0There is somewhat of a regular order i=
n Magic120Cell (the first sticker of each cell is the center, the next 12 a=
re the 2C pieces, then 3C follow, etc.), but this is not true in MC4D, wher=
e the stickers are created by a generic polytope slicing engine that will n=
ot produce stickers in a guaranteed, well-ordered manner. =A0Furthermore, t=
he cell ordering and cell orientations certainly won't match, and this =
will also affect the sticker numbering sequence.


In short, I'm afraid that without some complex cust=
om coding, it will not be possible to generate the transfer table you'd=
like. =A0So my apologies, but I think you are out of luck until one of the=
developers has time to add a piece finding feature to MC4D.


Take Care,
Roice


=3D"gmail_quote">On Sun, Feb 20, 2011 at 4:26 PM, Eduard =
<baumann@mcnet.ch>
wro=
te:

x #ccc solid;padding-left:1ex;">





Hi Roice, thanks very much for the answer.



I see both the transfer program and the evaluator need work..

I prefer the piece-evaluator (stickers can be in place without any worth).<=
br>
I see an evaluator problem for not layered methods as that in the RubikExpl=
orer for 3D.



The sticker-label-table for transfer is only about 7000 lines long.

Unpack the integer values is not a problem for me, but what about the numbe=
ring sequence. Is the numbering sequence in "Magic120Cell" and in=
MC4D topologically equivalent or are they both arbitrary and it is very di=
fficult to associate the two numberings?




I'm interested to start NOW with the faces in Magic120Cell where no mac=
ros are needed and the find option is very usefull. This will cost lot of h=
ours (weeks). I'm sure that I will not want to continue without macros =
(edges and corners). In this case the transfer is very important for me.>





--- In 4D_Cubing@yahoogroups.c=
om
, Roice Nelson <roice3@...> wrote:

>

> Hi Eduard,

>

> I can't give you the "table of stickers" you are asking =
for, because it

> would be huge. =A0I can briefly describe the log file encoding though.=
=A0In

> Magic120Cell, all the information for a twist is encoded into a 32-bit=


> integer, which is what you see in the log files. =A0There are 63 stick=
ers per

> cell, so 6 bits are required for that. =A07 bits are needed to record =
which of

> the 120 cells the sticker is on. =A01 bit is used to record the twist<=
br>
> direction, and another for whether or not it is a view rotation. =A0In=


> retrospect, I don't like that I packed it all into an integer. =A0=
It is

> compact, but people want to look in the log files and understand them,=
and

> this representation is opaque. =A0For the MagicTile log files I did a =
few

> weeks ago, I made it more reader friendly. =A0Andrey has suggested we =
come up

> with a standard format, so I'm sure some of these issues will aris=
e when

> that is discussed.

>

> MC4D has a different encoding of twists. =A0I didn't check the sou=
rce code

> (which is available

> online</browse/" target=3D"_blank">http://code.google.com/p/magiccube4d/source/bro=
wse/
>),

> but I'm pretty sure the last digit you were aski=
ng about is a

> bitmask<et=3D"_blank">http://en.wikipedia.org/wiki/Bitmask>representing the<=
br>
> slicemask of the twist (which slices were held down =
while

> twisting). =A0For the 120-cell puzzle with 3 stickers-per-side, this i=
s not an

> import piece of information, which is why it wasn't part of my twi=
st

> definition above. =A0But for other MC4D puzzles, it is important. =A0I=
f you had

> a 120-cell puzzle with 5 stickers per side, slicemask would need to be=


> included.

>

> Here are my other thoughts on this.

>

> - =A0I like the competitions and think they are good motivators, so ma=
king it

> such that more could participate is a worthy and positive goal. =A0(As=
an

> aside, I think it'd be cool if this could be more automated...that=
is, if

> the software could directly support logging solutions online without h=
uman

> intervention.)

> - =A0While effort could be expended on a log file transfer program, I =
think

> the better long term solution here would be to add the missing feature=
s to

> MC4D and retire the Magic120Cell code. =A0Also, I think the log filer>
> standardization Andrey has suggested would sidestep this need, assumin=
g the

> various implementations were updated to respect it.

> - =A0An "evaluator" feature could be added directly to MC4D,=
which would show

> the percentage completed on the puzzle. =A0You could calculate percent=
age

> complete on either a sticker or piece basis. =A0This feature request w=
ould be

> good to add to the issue

> tracker<s/list" target=3D"_blank">http://code.google.com/p/magiccube4d/issues/list<=
/a>>,

> so that it will be ready for when someone is motivat=
ed to work on it. =A0I do

> know it will be a difficult problem to handle generally in MC4D, due t=
o

> even-length puzzles where there aren't unmoving central stickers. =
=A0I ran

> into this when adding this feature to MC5D. =A0FYI, right now, the MC4=
D code

> just cycles through stickers on a face and checks whether they are all=
the

> same, and does this for each face. =A0Once it finds one different, it =
knows it

> is not solved and immediately returns. =A0So it doesn't need to th=
ink about

> how much of the puzzle is completed.

>

> Best,

> Roice

>

>

> On Sat, Feb 19, 2011 at 8:13 A=
M, Eduard <baumann@...> wrote:

>

> >

> > (a) Introduction

> >

> > The marvelaous 120-Cell in 4D.

> >

> > The 4D Regulars are very sympathic models of perfect democratic s=
ocieties

> > with perfectly equal individuals. Each has an equal number of nei=
ghbours in

> > equal constellation. This number is 4 for the 5-Cell, 6 for the h=
ypercube (8

> > `individuals') and 12 for the 120-Cell (120 `individuals'=
=3D society).

> >

> > A cluster of bees in winter has to arrange changes of roles (inne=
r / outer

> > places in the cluster). Everybody wants be in the warmer inner sp=
ace. No

> > such problems in 4D at least for 120 bees housed in the 120-Cell.=
Everybody

> > is equally surrounded by 12 neighbours. Perhaps arrange the bees =
in 3D in a

> > infinite grid to avoid social problems.

> >

> > Let me use the abreviations =84Magic" for the program Magic1=
20Cell and

> > =84Hyper" for the Hypermeaminx puzzle in MC4D.

> >

> >

> > (b) Combine Magic and Hyper.

> >

> > I think Magic and Hyper cannot share their log files.

> >

> > Complementarity: Magic has finding help and no macro, Hyper has n=
o finding

> > help but macro.

> >

> > I need both!

> >

> > How about a *transfer* program?

> >

> > Roice: can you give me a table with the two corresponding labelin=
gs of

> > stickers in Magic and Hyper? I need also to know the significatio=
n of the

> > last digit of the numbers in Magic log file (2 clockwise and 4 an=
ticlockwise

> > for faces, what is 6 and 8?).

> >

> >

> > (c) Partial HOF

> >

> > The HOF for the 120-Cell has only two entries until now. Noel Cha=
lmers and

> > Matt Galla (great performer). In order to achive more participant=
s (about

> > 400 as in the Al Zimmerman contests) I propose to install HOF for=
partial

> > results.

> >

> > For this I need an *evaluator*, a program which calculates the pe=
rcentage

> > of cubies in place and well oriented from the log file. The code =
must

> > already existe for the checking and emitting "Congratulation=
s" in MC4D.

> >

> > With this evaluator a ranking list is possible as in the Al Zimme=
rman

> > contests (take best results of each participant).

> >

> > This can be a good motivation to get in touch with the 120-Cell a=
nd live a

> > moment in the world of this 120 individuals (dodecahedra).

> >

> > If I get the evaluator and the incoming log files

> >

> > I propose to do the managing this of partial HOF in
tp://superliminal.com/wiki(in" target=3D"_blank">superliminal.com/wiki(ina> protected pages).

> >

> > Doing only the 2 colored faces in the 120-Cell is already demandi=
ng because

> > you have to get a good feeling of the neighbourhoods and soon to =
use

> > commutators to avoid the disturbing of already placed cubies.

> >

> > If this partial HOF is working I propose to do promotion in (1) R=
oice's

> > description of Magic120Cell, (2) Roice's description of MC4D,=
(3)

> > Superliminal.com/wiki and (4) in the "4D cubing" forum.=


> >

> > What do you think all?

>









------------------------------------



Yahoo! Groups Links



<*> To visit your group on the web, go to:

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--0016e6da98b90002dd049cbece0e--




From: "Eduard Baumann" <baumann@mcnet.ch>
Date: Mon, 21 Feb 2011 01:05:04 +0100
Subject: Re: [MC4D] Social dream



------=_NextPart_000_0006_01CBD163.5FA18720
Content-Type: text/plain;
charset="Windows-1252"
Content-Transfer-Encoding: quoted-printable

Okay, thanks, I understand.
I will wait with tackling the 120-cell.
Ed

----- Original Message -----=20
From: Roice Nelson=20
To: 4D_Cubing@yahoogroups.com=20
Sent: Monday, February 21, 2011 12:07 AM
Subject: Re: [MC4D] Social dream


=20=20=20=20
Hi Eduard,



I'm sorry, but I do not think what you are asking for is trivial to do. =
The sticker numbering sequence is indeed different among the two programs. =
There is somewhat of a regular order in Magic120Cell (the first sticker of=
each cell is the center, the next 12 are the 2C pieces, then 3C follow, et=
c.), but this is not true in MC4D, where the stickers are created by a gene=
ric polytope slicing engine that will not produce stickers in a guaranteed,=
well-ordered manner. Furthermore, the cell ordering and cell orientations=
certainly won't match, and this will also affect the sticker numbering seq=
uence.


In short, I'm afraid that without some complex custom coding, it will not=
be possible to generate the transfer table you'd like. So my apologies, b=
ut I think you are out of luck until one of the developers has time to add =
a piece finding feature to MC4D.


Take Care,
Roice



On Sun, Feb 20, 2011 at 4:26 PM, Eduard wrote:




Hi Roice, thanks very much for the answer.

I see both the transfer program and the evaluator need work..
I prefer the piece-evaluator (stickers can be in place without any wort=
h).
I see an evaluator problem for not layered methods as that in the Rubik=
Explorer for 3D.

The sticker-label-table for transfer is only about 7000 lines long.
Unpack the integer values is not a problem for me, but what about the n=
umbering sequence. Is the numbering sequence in "Magic120Cell" and in MC4D =
topologically equivalent or are they both arbitrary and it is very difficul=
t to associate the two numberings?

I'm interested to start NOW with the faces in Magic120Cell where no mac=
ros are needed and the find option is very usefull. This will cost lot of h=
ours (weeks). I'm sure that I will not want to continue without macros (edg=
es and corners). In this case the transfer is very important for me.



--- In 4D_Cubing@yahoogroups.com, Roice Nelson wrote:
>
> Hi Eduard,
>
> I can't give you the "table of stickers" you are asking for, because =
it
> would be huge. I can briefly describe the log file encoding though. =
In
> Magic120Cell, all the information for a twist is encoded into a 32-bi=
t
> integer, which is what you see in the log files. There are 63 sticke=
rs per
> cell, so 6 bits are required for that. 7 bits are needed to record w=
hich of
> the 120 cells the sticker is on. 1 bit is used to record the twist
> direction, and another for whether or not it is a view rotation. In
> retrospect, I don't like that I packed it all into an integer. It is
> compact, but people want to look in the log files and understand them=
, and
> this representation is opaque. For the MagicTile log files I did a f=
ew
> weeks ago, I made it more reader friendly. Andrey has suggested we c=
ome up
> with a standard format, so I'm sure some of these issues will arise w=
hen
> that is discussed.
>
> MC4D has a different encoding of twists. I didn't check the source c=
ode
> (which is available

> online),

> but I'm pretty sure the last digit you were asking about is a

> bitmaskrepresenting the

> slicemask of the twist (which slices were held down while
> twisting). For the 120-cell puzzle with 3 stickers-per-side, this is=
not an
> import piece of information, which is why it wasn't part of my twist
> definition above. But for other MC4D puzzles, it is important. If y=
ou had
> a 120-cell puzzle with 5 stickers per side, slicemask would need to b=
e
> included.
>
> Here are my other thoughts on this.
>
> - I like the competitions and think they are good motivators, so mak=
ing it
> such that more could participate is a worthy and positive goal. (As =
an
> aside, I think it'd be cool if this could be more automated...that is=
, if
> the software could directly support logging solutions online without =
human
> intervention.)
> - While effort could be expended on a log file transfer program, I t=
hink
> the better long term solution here would be to add the missing featur=
es to
> MC4D and retire the Magic120Cell code. Also, I think the log file
> standardization Andrey has suggested would sidestep this need, assumi=
ng the
> various implementations were updated to respect it.
> - An "evaluator" feature could be added directly to MC4D, which woul=
d show
> the percentage completed on the puzzle. You could calculate percenta=
ge
> complete on either a sticker or piece basis. This feature request wo=
uld be
> good to add to the issue

> tracker,

> so that it will be ready for when someone is motivated to work on it.=
I do
> know it will be a difficult problem to handle generally in MC4D, due =
to
> even-length puzzles where there aren't unmoving central stickers. I =
ran
> into this when adding this feature to MC5D. FYI, right now, the MC4D=
code
> just cycles through stickers on a face and checks whether they are al=
l the
> same, and does this for each face. Once it finds one different, it k=
nows it
> is not solved and immediately returns. So it doesn't need to think a=
bout
> how much of the puzzle is completed.
>
> Best,
> Roice
>
>

> On Sat, Feb 19, 2011 at 8:13 AM, Eduard wrote:
>
> >
> > (a) Introduction
> >
> > The marvelaous 120-Cell in 4D.
> >
> > The 4D Regulars are very sympathic models of perfect democratic soc=
ieties
> > with perfectly equal individuals. Each has an equal number of neigh=
bours in
> > equal constellation. This number is 4 for the 5-Cell, 6 for the hyp=
ercube (8
> > `individuals') and 12 for the 120-Cell (120 `individuals' =3D socie=
ty).
> >
> > A cluster of bees in winter has to arrange changes of roles (inner =
/ outer
> > places in the cluster). Everybody wants be in the warmer inner spac=
e. No
> > such problems in 4D at least for 120 bees housed in the 120-Cell. E=
verybody
> > is equally surrounded by 12 neighbours. Perhaps arrange the bees in=
3D in a
> > infinite grid to avoid social problems.
> >
> > Let me use the abreviations =84Magic" for the program Magic120Cell =
and
> > =84Hyper" for the Hypermeaminx puzzle in MC4D.
> >
> >
> > (b) Combine Magic and Hyper.
> >
> > I think Magic and Hyper cannot share their log files.
> >
> > Complementarity: Magic has finding help and no macro, Hyper has no =
finding
> > help but macro.
> >
> > I need both!
> >
> > How about a *transfer* program?
> >
> > Roice: can you give me a table with the two corresponding labelings=
of
> > stickers in Magic and Hyper? I need also to know the signification =
of the
> > last digit of the numbers in Magic log file (2 clockwise and 4 anti=
clockwise
> > for faces, what is 6 and 8?).
> >
> >
> > (c) Partial HOF
> >
> > The HOF for the 120-Cell has only two entries until now. Noel Chalm=
ers and
> > Matt Galla (great performer). In order to achive more participants =
(about
> > 400 as in the Al Zimmerman contests) I propose to install HOF for p=
artial
> > results.
> >
> > For this I need an *evaluator*, a program which calculates the perc=
entage
> > of cubies in place and well oriented from the log file. The code mu=
st
> > already existe for the checking and emitting "Congratulations" in M=
C4D.
> >
> > With this evaluator a ranking list is possible as in the Al Zimmerm=
an
> > contests (take best results of each participant).
> >
> > This can be a good motivation to get in touch with the 120-Cell and=
live a
> > moment in the world of this 120 individuals (dodecahedra).
> >
> > If I get the evaluator and the incoming log files
> >
> > I propose to do the managing this of partial HOF in superliminal.co=
m/wiki(in protected pages).
> >
> > Doing only the 2 colored faces in the 120-Cell is already demanding=
because
> > you have to get a good feeling of the neighbourhoods and soon to us=
e
> > commutators to avoid the disturbing of already placed cubies.
> >
> > If this partial HOF is working I propose to do promotion in (1) Roi=
ce's
> > description of Magic120Cell, (2) Roice's description of MC4D, (3)
> > Superliminal.com/wiki and (4) in the "4D cubing" forum.
> >
> > What do you think all?
>





------------------------------------

Yahoo! Groups Links







=20=20
------=_NextPart_000_0006_01CBD163.5FA18720
Content-Type: text/html;
charset="Windows-1252"
Content-Transfer-Encoding: quoted-printable



pe>


Okay, thanks, I understand.

I will wait with tackling the=20
120-cell.

Ed

 

style=3D"BORDER-LEFT: #000000 2px solid; PADDING-LEFT: 5px; PADDING-RIGHT: =
0px; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px">
----- Original Message -----

style=3D"FONT: 10pt arial; BACKGROUND: #e4e4e4; font-color: black">Fro=
m:
=20
Roice Nelson=
=20

To: ps.com=20
href=3D"mailto:4D_Cubing@yahoogroups.com">4D_Cubing@yahoogroups.com
<=
/DIV>
Sent: Monday, February 21, 2011 12=
:07=20
AM

Subject: Re: [MC4D] Social dreamDIV>

 =20

Hi Eduard,



I'm sorry, but I do not think what you are asking for is trivial to =
do.=20
 The sticker numbering sequence is indeed different among the two=20
programs.  There is somewhat of a regular order in Magic120Cell (the=
=20
first sticker of each cell is the center, the next 12 are the 2C pieces, =
then=20
3C follow, etc.), but this is not true in MC4D, where the stickers are cr=
eated=20
by a generic polytope slicing engine that will not produce stickers in a=
=20
guaranteed, well-ordered manner.  Furthermore, the cell ordering and=
cell=20
orientations certainly won't match, and this will also affect the sticker=
=20
numbering sequence.



In short, I'm afraid that without some complex custom coding, it wil=
l not=20
be possible to generate the transfer table you'd like.  So my apolog=
ies,=20
but I think you are out of luck until one of the developers has time to a=
dd a=20
piece finding feature to MC4D.



Take Care,

Roice




On Sun, Feb 20, 2011 at 4:26 PM, Eduard dir=3Dltr><baumann@mcnet.ch>=
;=20
wrote:

class=3Dgmail_quote>


Hi Roice, thanks very much for the=20
answer.

I see both the transfer program and the evaluator need=20
work..
I prefer the piece-evaluator (stickers can be in place withou=
t any=20
worth).
I see an evaluator problem for not layered methods as that i=
n the=20
RubikExplorer for 3D.

The sticker-label-table for transfer is on=
ly=20
about 7000 lines long.
Unpack the integer values is not a problem fo=
r me,=20
but what about the numbering sequence. Is the numbering sequence in=20
"Magic120Cell" and in MC4D topologically equivalent or are they both=20
arbitrary and it is very difficult to associate the two=20
numberings?

I'm interested to start NOW with the faces in=20
Magic120Cell where no macros are needed and the find option is very use=
full.=20
This will cost lot of hours (weeks). I'm sure that I will not want to=20
continue without macros (edges and corners). In this case the transfer =
is=20
very important for me.



--- In href=3D"mailto:4D_Cubing@yahoogroups.com">4D_Cubing@yahoogroups.com=
, Roice=20
Nelson <roice3@...> wrote:
>
> Hi Eduard,
>
=
>=20
I can't give you the "table of stickers" you are asking for, because=20
it
> would be huge.  I can briefly describe the log file enc=
oding=20
though.  In
> Magic120Cell, all the information for a twist =
is=20
encoded into a 32-bit
> integer, which is what you see in the log=
=20
files.  There are 63 stickers per
> cell, so 6 bits are requ=
ired=20
for that.  7 bits are needed to record which of
> the 120 ce=
lls=20
the sticker is on.  1 bit is used to record the twist
>=20
direction, and another for whether or not it is a view rotation.=20
 In
> retrospect, I don't like that I packed it all into an=
=20
integer.  It is
> compact, but people want to look in the lo=
g=20
files and understand them, and
> this representation is opaque.=20
 For the MagicTile log files I did a few
> weeks ago, I made=
it=20
more reader friendly.  Andrey has suggested we come up
> wit=
h a=20
standard format, so I'm sure some of these issues will arise when
&g=
t;=20
that is discussed.
>
> MC4D has a different encoding of twi=
sts.=20
 I didn't check the source code
> (which is=20
available
> online< href=3D"http://code.google.com/p/magiccube4d/source/browse/"=20
target=3D_blank>http://code.google.com/p/magiccube4d/source/browse/=
>),

> but I'm pretty sure the last digit you were asking=
about=20
is a
> bitmask<itmask"=20
target=3D_blank>http://en.wikipedia.org/wiki/Bitmask
>representin=
g=20
the

> slicemask of the twist (which slices were held dow=
n=20
while
> twisting).  For the 120-cell puzzle with 3=20
stickers-per-side, this is not an
> import piece of information, =
which=20
is why it wasn't part of my twist
> definition above.  But f=
or=20
other MC4D puzzles, it is important.  If you had
> a 120-cel=
l=20
puzzle with 5 stickers per side, slicemask would need to be
>=20
included.
>
> Here are my other thoughts on=20
this.
>
> -  I like the competitions and think they ar=
e=20
good motivators, so making it
> such that more could participate =
is a=20
worthy and positive goal.  (As an
> aside, I think it'd be c=
ool=20
if this could be more automated...that is, if
> the software coul=
d=20
directly support logging solutions online without human
>=20
intervention.)
> -  While effort could be expended on a log =
file=20
transfer program, I think
> the better long term solution here wo=
uld=20
be to add the missing features to
> MC4D and retire the Magic120C=
ell=20
code.  Also, I think the log file
> standardization Andrey h=
as=20
suggested would sidestep this need, assuming the
> various=20
implementations were updated to respect it.
> -  An "evaluat=
or"=20
feature could be added directly to MC4D, which would show
> the=20
percentage completed on the puzzle.  You could calculate=20
percentage
> complete on either a sticker or piece basis.  T=
his=20
feature request would be
> good to add to the issue
>=
=20
tracker<=20
target=3D_blank>http://code.google.com/p/magiccube4d/issues/list
>=
;,

> so that it will be ready for when someone is motiv=
ated to=20
work on it.  I do
> know it will be a difficult problem to h=
andle=20
generally in MC4D, due to
> even-length puzzles where there aren'=
t=20
unmoving central stickers.  I ran
> into this when adding th=
is=20
feature to MC5D.  FYI, right now, the MC4D code
> just cycle=
s=20
through stickers on a face and checks whether they are all the
> =
same,=20
and does this for each face.  Once it finds one different, it know=
s=20
it
> is not solved and immediately returns.  So it doesn't n=
eed=20
to think about
> how much of the puzzle is completed.
>
=
>=20
Best,
> Roice
>
>



> On Sat, Feb 19, 2011 at 8:13 AM, Eduard=20
<baumann@...> wrote:
>
> >
> > (a)=20
Introduction
> >
> > The marvelaous 120-Cell in=20
4D.
> >
> > The 4D Regulars are very sympathic models=
of=20
perfect democratic societies
> > with perfectly equal individu=
als.=20
Each has an equal number of neighbours in
> > equal constellat=
ion.=20
This number is 4 for the 5-Cell, 6 for the hypercube (8
> >=20
`individuals') and 12 for the 120-Cell (120 `individuals' =3D=20
society).
> >
> > A cluster of bees in winter has to=
=20
arrange changes of roles (inner / outer
> > places in the clus=
ter).=20
Everybody wants be in the warmer inner space. No
> > such prob=
lems=20
in 4D at least for 120 bees housed in the 120-Cell. Everybody
> &=
gt;=20
is equally surrounded by 12 neighbours. Perhaps arrange the bees in 3D =
in=20
a
> > infinite grid to avoid social problems.
> >
=
>=20
> Let me use the abreviations =84Magic" for the program Magic120Cell=
=20
and
> > =84Hyper" for the Hypermeaminx puzzle in MC4D.
>=
=20
>
> >
> > (b) Combine Magic and Hyper.
>=20
>
> > I think Magic and Hyper cannot share their log=20
files.
> >
> > Complementarity: Magic has finding hel=
p and=20
no macro, Hyper has no finding
> > help but macro.
>=20
>
> > I need both!
> >
> > How about a=20
*transfer* program?
> >
> > Roice: can you give me a =
table=20
with the two corresponding labelings of
> > stickers in Magic =
and=20
Hyper? I need also to know the signification of the
> > last d=
igit=20
of the numbers in Magic log file (2 clockwise and 4 anticlockwise
&g=
t;=20
> for faces, what is 6 and 8?).
> >
> >
> &g=
t;=20
(c) Partial HOF
> >
> > The HOF for the 120-Cell has =
only=20
two entries until now. Noel Chalmers and
> > Matt Galla (great=
=20
performer). In order to achive more participants (about
> > 40=
0 as=20
in the Al Zimmerman contests) I propose to install HOF for partial
&=
gt;=20
> results.
> >
> > For this I need an *evaluator*,=
a=20
program which calculates the percentage
> > of cubies in place=
and=20
well oriented from the log file. The code must
> > already exi=
ste=20
for the checking and emitting "Congratulations" in MC4D.
>=20
>
> > With this evaluator a ranking list is possible as in =
the=20
Al Zimmerman
> > contests (take best results of each=20
participant).
> >
> > This can be a good motivation t=
o get=20
in touch with the 120-Cell and live a
> > moment in the world =
of=20
this 120 individuals (dodecahedra).
> >
> > If I get =
the=20
evaluator and the incoming log files
> >
> > I propos=
e to=20
do the managing this of partial HOF in href=3D"http://superliminal.com/wiki(in"=20
target=3D_blank>superliminal.com/wiki(in protected pages).
>=
=20
>
> > Doing only the 2 colored faces in the 120-Cell is alr=
eady=20
demanding because
> > you have to get a good feeling of the=20
neighbourhoods and soon to use
> > commutators to avoid the=20
disturbing of already placed cubies.
> >
> > If this=
=20
partial HOF is working I propose to do promotion in (1) Roice's
>=
>=20
description of Magic120Cell, (2) Roice's description of MC4D, (3)
&g=
t;=20
> Superliminal.com/wiki and (4) in the "4D cubing" forum.
>=20
>
> > What do you think=20
all?
>




---------------------------=
---------

Yahoo!=20
Groups Links

<*> To visit your group on the web, go=20
to:
   "=20
target=3D_blank>http://groups.yahoo.com/group/4D_Cubing/


<=
;*>=20
Your email settings:
   Individual Email |=20
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<*> To change settings online go to:
 =
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  target=3D_blank>http://groups.yahoo.com/group/4D_Cubing/join
&nb=
sp;=20
 (Yahoo! ID required)

<*> To change settings via=20
email:
    href=3D"mailto:4D_Cubing-digest@yahoogroups.com">4D_Cubing-digest@yahoo=
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<*>=20
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TE>




------=_NextPart_000_0006_01CBD163.5FA18720--




From: Melinda Green <melinda@superliminal.com>
Date: Sun, 20 Feb 2011 16:16:39 -0800
Subject: Re: [MC4D] Social dream



Hello Eduard,

Please be aware that if you put substantial work into a 120 cell
solution in Roice's implementation, that you will likely either have to
wait for someone to support his log format in MC4D (or write a
stand-alone converter) or do the coding yourself. If you do it
yourself, I encourage you to write it in Java and possibly even do it by
extending MC4D to be able to read and possibly write Roice's format.
It's fine to do it as a stand-alone program too because it should be
easy for someone to add it later into MC4D so long as you write it in
Java. Mostly I just want to make sure that you understand the risk of
doing weeks of work with M120C in order to use its piece-finder and then
being stuck waiting for that functionality in MC4D in order to use it's
macro ability to finish the job.

Good luck with whatever you decide to do!
-Melinda

On 2/20/2011 2:26 PM, Eduard wrote:
>
>
> Hi Roice, thanks very much for the answer.
>
> I see both the transfer program and the evaluator need work..
> I prefer the piece-evaluator (stickers can be in place without any worth).
> I see an evaluator problem for not layered methods as that in the RubikExplorer for 3D.
>
> The sticker-label-table for transfer is only about 7000 lines long.
> Unpack the integer values is not a problem for me, but what about the numbering sequence. Is the numbering sequence in "Magic120Cell" and in MC4D topologically equivalent or are they both arbitrary and it is very difficult to associate the two numberings?
>
> I'm interested to start NOW with the faces in Magic120Cell where no macros are needed and the find option is very usefull. This will cost lot of hours (weeks). I'm sure that I will not want to continue without macros (edges and corners). In this case the transfer is very important for me.
>
>
> --- In 4D_Cubing@yahoogroups.com, Roice Nelson wrote:
>> Hi Eduard,
>>
>> I can't give you the "table of stickers" you are asking for, because it
>> would be huge. I can briefly describe the log file encoding though. In
>> Magic120Cell, all the information for a twist is encoded into a 32-bit
>> integer, which is what you see in the log files. There are 63 stickers per
>> cell, so 6 bits are required for that. 7 bits are needed to record which of
>> the 120 cells the sticker is on. 1 bit is used to record the twist
>> direction, and another for whether or not it is a view rotation. In
>> retrospect, I don't like that I packed it all into an integer. It is
>> compact, but people want to look in the log files and understand them, and
>> this representation is opaque. For the MagicTile log files I did a few
>> weeks ago, I made it more reader friendly. Andrey has suggested we come up
>> with a standard format, so I'm sure some of these issues will arise when
>> that is discussed.
>>
>> MC4D has a different encoding of twists. I didn't check the source code
>> (which is available
>> online),
>> but I'm pretty sure the last digit you were asking about is a
>> bitmaskrepresenting the
>> slicemask of the twist (which slices were held down while
>> twisting). For the 120-cell puzzle with 3 stickers-per-side, this is not an
>> import piece of information, which is why it wasn't part of my twist
>> definition above. But for other MC4D puzzles, it is important. If you had
>> a 120-cell puzzle with 5 stickers per side, slicemask would need to be
>> included.
>>
>> Here are my other thoughts on this.
>>
>> - I like the competitions and think they are good motivators, so making it
>> such that more could participate is a worthy and positive goal. (As an
>> aside, I think it'd be cool if this could be more automated...that is, if
>> the software could directly support logging solutions online without human
>> intervention.)
>> - While effort could be expended on a log file transfer program, I think
>> the better long term solution here would be to add the missing features to
>> MC4D and retire the Magic120Cell code. Also, I think the log file
>> standardization Andrey has suggested would sidestep this need, assuming the
>> various implementations were updated to respect it.
>> - An "evaluator" feature could be added directly to MC4D, which would show
>> the percentage completed on the puzzle. You could calculate percentage
>> complete on either a sticker or piece basis. This feature request would be
>> good to add to the issue
>> tracker,
>> so that it will be ready for when someone is motivated to work on it. I do
>> know it will be a difficult problem to handle generally in MC4D, due to
>> even-length puzzles where there aren't unmoving central stickers. I ran
>> into this when adding this feature to MC5D. FYI, right now, the MC4D code
>> just cycles through stickers on a face and checks whether they are all the
>> same, and does this for each face. Once it finds one different, it knows it
>> is not solved and immediately returns. So it doesn't need to think about
>> how much of the puzzle is completed.
>>
>> Best,
>> Roice
>>




From: "Andrey" <andreyastrelin@yahoo.com>
Date: Mon, 21 Feb 2011 07:11:34 -0000
Subject: Re: [MC4D] Social dream



Hi all,
About piece finding and percentage of solving, there is a problem in the =
most puzzles: if puzzle has no unmoving center of the cell, you cannot say =
what is the proper color for this cell. So there is no way to say "what is =
the place for this piece", "where this piece should go" and "how many piece=
s/stickers are in their places". Program can "guess" colors for faces (by m=
ajority of colors), but is may lead to strange situatons: you solve somethi=
ng like simplex, get one twisted corner piece, and can't solve it without r=
eassigning colors to cells. But the program keeps telling you that you are =
going from the correct solution, and number of solved pieces is decreasing =
(until you get enough stickers in their new cells)=20
So I used alternative approach to piece-finding in MC7D. It works, but it=
's much less intuitive than "click in piece and see where it goes".

As for the log files, my first idea is the following.
Let we have some puzzle based on uniform polytope. Now we don't consider =
shape-transformers, so form of puzzle remains the same after each twist.
Cutting hyperplanes are ortogonal to some axes (going through the center =
of the puzzle). These axes may contain centers of cells, 2D faces, middles =
of edges and vertices of the puzzle, but it doesn't matter. What is importa=
nt, the set of axes for the puzzle is a subset of symmetry/rotation axes of=
the puzzle body. There are not many symmetry sets in 4D:
- symmetries of 5-cell (15 axes)
- symmetries of bitruncated 5-cell (70 axes?)
- symmetries of 8-cell (40 axes)
- symmetries of 24-cell (120 axes)
- symmetries of bitruncated 24-cell (624 axes?)
- symmetries of 120-cell (1320 axes)
- symmetries of duoprism [n]x[k] (n+k axes?)
- symmetries of duoprism [n]x[n] (2*n+n^2 axes?)

We can enumerate axes for every case in some agreed order.

For every axis we have number and positions of cutting planes. They define =
number and connections of stickers, but almost don't influence rotation des=
criptions. We need to define mask of layers for the twist, and for that we =
must know only one thing - what is the maximal number M of layers there is =
from the center to the surface (for all axes) - not including central layer=
. For example, for 3^4 tesseract it will be 1, and for 3^4 with diagonal cu=
ttings x=B1y=B1z=B1w=3D{-2,0,2} (for x,y,z,w=3D{-1,1}) it will be 2 (there =
are 3 layers orthogonal to (0,0,0,1) and 4 layers orthogonal to (1,1,1,1) )=
. If such number M is defined, we enumerate layers by each axis so that cen=
tral layer (if it exists) has number M. If thare is no central layer, M is =
skipped. For the example above layers parallel to cells will have numbers 1=
,2,3 and layers in 0D direction (orthogonal to (1,1,1,1)) will be 0,1,3,4.=
=20
This way we define the mask of the twist.=20

To define the twist we need two more things - direction of 3D axis of twist=
and twisting angle. My guess is that 3D axis is always one of symmetry axe=
s that is perpendicular to the layer axis, so it is enumerated in our set. =
The problem will be with the angle.

Some puzzles (such as 3x3x4x4, or alternated puzzles like snub 24-cell) may=
have restricted set of twists enabled by the axes set. So we can't just wr=
ite "turn on smallest possible angle clockwise", we need to define angle ex=
plicitly. I suggest to select some number D for every axes set, that will b=
e common divisor for all twist orders (not necessarily the least) - 12 for =
simplex, hypercube or 24-cell, 60 for 120-cell, [n,k,2] for duoprism, inclu=
de it in the set description and write angles assuming D=3D360 deg.
So every twist will be described by 4 numbers:
- direction of main axis (orthogonal to the cutting plane)
- direction of 3D axis (it's perpendicular to the main axis)
- rotation angle
- layers mask

For example, 120-deg rotation of 3rd layer of 4^4 may have the form
A1:A2:4:8, where A1=3D(1,0,0,0) and A2=3D(0,1,-1,1) (4=3D12/3, 8=3D2^3)

I don't want to include complete stickers mask in the description (stickers=
order and description may be different for different implementations), and=
don't see good way to define the starting situation. Of course, we can fin=
d the description for every sticker It may include 4 cutting planes that gi=
ve its vertex, and a mask that gives position of the sticker relative to th=
ese planes. But definition of the puzzle state is such terms will be terrib=
le. I afraid that we will be able to keep only possible positions defined b=
y the twists sequence.

All the other things - body shape, coloring, position of cutting planes, ma=
sk/description of stickers, not included in puzzle (and the shape of the re=
maining stickers), bandaging and so on - it will be in the log header and i=
ts interpretation (=3D puzzle description) is another story.

Andrey





From: "Eduard Baumann" <baumann@mcnet.ch>
Date: Mon, 21 Feb 2011 13:47:00 +0100
Subject: Re: [MC4D] Social dream



------=_NextPart_000_0029_01CBD1CD.D072B3B0
Content-Type: text/plain;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

Fortunatly the 120-cell HAS unmoving center of the cells.
Ed

----- Original Message -----=20
From: Andrey=20
To: 4D_Cubing@yahoogroups.com=20
Sent: Monday, February 21, 2011 8:11 AM
Subject: Re: [MC4D] Social dream


=20=20=20=20
Hi all,
About piece finding and percentage of solving, there is a problem in the =
most puzzles: if puzzle has no unmoving center of the cell, you cannot say =
what is the proper color for this cell. So there is no way to say "what is =
the place for this piece", "where this piece should go" and "how many piece=
s/stickers are in their places". Program can "guess" colors for faces (by m=
ajority of colors), but is may lead to strange situatons: you solve somethi=
ng like simplex, get one twisted corner piece, and can't solve it without r=
eassigning colors to cells. But the program keeps telling you that you are =
going from the correct solution, and number of solved pieces is decreasing =
(until you get enough stickers in their new cells)=20
So I used alternative approach to piece-finding in MC7D. It works, but it=
's much less intuitive than "click in piece and see where it goes".

As for the log files, my first idea is the following.
Let we have some puzzle based on uniform polytope. Now we don't consider =
shape-transformers, so form of puzzle remains the same after each twist.
Cutting hyperplanes are ortogonal to some axes (going through the center =
of the puzzle). These axes may contain centers of cells, 2D faces, middles =
of edges and vertices of the puzzle, but it doesn't matter. What is importa=
nt, the set of axes for the puzzle is a subset of symmetry/rotation axes of=
the puzzle body. There are not many symmetry sets in 4D:
- symmetries of 5-cell (15 axes)
- symmetries of bitruncated 5-cell (70 axes?)
- symmetries of 8-cell (40 axes)
- symmetries of 24-cell (120 axes)
- symmetries of bitruncated 24-cell (624 axes?)
- symmetries of 120-cell (1320 axes)
- symmetries of duoprism [n]x[k] (n+k axes?)
- symmetries of duoprism [n]x[n] (2*n+n^2 axes?)

We can enumerate axes for every case in some agreed order.

For every axis we have number and positions of cutting planes. They defin=
e number and connections of stickers, but almost don't influence rotation d=
escriptions. We need to define mask of layers for the twist, and for that w=
e must know only one thing - what is the maximal number M of layers there i=
s from the center to the surface (for all axes) - not including central lay=
er. For example, for 3^4 tesseract it will be 1, and for 3^4 with diagonal =
cuttings x=B1y=B1z=B1w=3D{-2,0,2} (for x,y,z,w=3D{-1,1}) it will be 2 (ther=
e are 3 layers orthogonal to (0,0,0,1) and 4 layers orthogonal to (1,1,1,1)=
). If such number M is defined, we enumerate layers by each axis so that c=
entral layer (if it exists) has number M. If thare is no central layer, M i=
s skipped. For the example above layers parallel to cells will have numbers=
1,2,3 and layers in 0D direction (orthogonal to (1,1,1,1)) will be 0,1,3,4=
.=20
This way we define the mask of the twist.=20

To define the twist we need two more things - direction of 3D axis of twi=
st and twisting angle. My guess is that 3D axis is always one of symmetry a=
xes that is perpendicular to the layer axis, so it is enumerated in our set=
. The problem will be with the angle.

Some puzzles (such as 3x3x4x4, or alternated puzzles like snub 24-cell) m=
ay have restricted set of twists enabled by the axes set. So we can't just =
write "turn on smallest possible angle clockwise", we need to define angle =
explicitly. I suggest to select some number D for every axes set, that will=
be common divisor for all twist orders (not necessarily the least) - 12 fo=
r simplex, hypercube or 24-cell, 60 for 120-cell, [n,k,2] for duoprism, inc=
lude it in the set description and write angles assuming D=3D360 deg.
So every twist will be described by 4 numbers:
- direction of main axis (orthogonal to the cutting plane)
- direction of 3D axis (it's perpendicular to the main axis)
- rotation angle
- layers mask

For example, 120-deg rotation of 3rd layer of 4^4 may have the form
A1:A2:4:8, where A1=3D(1,0,0,0) and A2=3D(0,1,-1,1) (4=3D12/3, 8=3D2^3)

I don't want to include complete stickers mask in the description (sticke=
rs order and description may be different for different implementations), a=
nd don't see good way to define the starting situation. Of course, we can f=
ind the description for every sticker It may include 4 cutting planes that =
give its vertex, and a mask that gives position of the sticker relative to =
these planes. But definition of the puzzle state is such terms will be terr=
ible. I afraid that we will be able to keep only possible positions defined=
by the twists sequence.

All the other things - body shape, coloring, position of cutting planes, =
mask/description of stickers, not included in puzzle (and the shape of the =
remaining stickers), bandaging and so on - it will be in the log header and=
its interpretation (=3D puzzle description) is another story.

Andrey



=20=20
------=_NextPart_000_0029_01CBD1CD.D072B3B0
Content-Type: text/html;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable



>


Fortunatly the 120-cell HAS unmoving center of the cells.

Ed

 

style=3D"BORDER-LEFT: #000000 2px solid; PADDING-LEFT: 5px; PADDING-RIGHT: =
0px; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px">
----- Original Message -----

style=3D"FONT: 10pt arial; BACKGROUND: #e4e4e4; font-color: black">Fro=
m:
=20
href=3D"mailto:andreyastrelin@yahoo.com">Andrey

To: ps.com=20
href=3D"mailto:4D_Cubing@yahoogroups.com">4D_Cubing@yahoogroups.com
<=
/DIV>
Sent: Monday, February 21, 2011 8:=
11=20
AM

Subject: Re: [MC4D] Social dreamDIV>

 =20

Hi all,
About piece finding and percentage of solving, there is a=20
problem in the most puzzles: if puzzle has no unmoving center of the cell=
, you=20
cannot say what is the proper color for this cell. So there is no way to =
say=20
"what is the place for this piece", "where this piece should go" and "how=
many=20
pieces/stickers are in their places". Program can "guess" colors for face=
s (by=20
majority of colors), but is may lead to strange situatons: you solve some=
thing=20
like simplex, get one twisted corner piece, and can't solve it without=20
reassigning colors to cells. But the program keeps telling you that you a=
re=20
going from the correct solution, and number of solved pieces is decreasin=
g=20
(until you get enough stickers in their new cells)
So I used alternat=
ive=20
approach to piece-finding in MC7D. It works, but it's much less intuitive=
than=20
"click in piece and see where it goes".

As for the log files, my f=
irst=20
idea is the following.
Let we have some puzzle based on uniform polyto=
pe.=20
Now we don't consider shape-transformers, so form of puzzle remains the s=
ame=20
after each twist.
Cutting hyperplanes are ortogonal to some axes (goin=
g=20
through the center of the puzzle). These axes may contain centers of cell=
s, 2D=20
faces, middles of edges and vertices of the puzzle, but it doesn't matter=
.=20
What is important, the set of axes for the puzzle is a subset of=20
symmetry/rotation axes of the puzzle body. There are not many symmetry se=
ts in=20
4D:
- symmetries of 5-cell (15 axes)
- symmetries of bitruncated 5-=
cell=20
(70 axes?)
- symmetries of 8-cell (40 axes)
- symmetries of 24-cell=
(120=20
axes)
- symmetries of bitruncated 24-cell (624 axes?)
- symmetries =
of=20
120-cell (1320 axes)
- symmetries of duoprism [n]x[k] (n+k axes?)
-=
=20
symmetries of duoprism [n]x[n] (2*n+n^2 axes?)

We can enumerate ax=
es=20
for every case in some agreed order.

For every axis we have number=
and=20
positions of cutting planes. They define number and connections of sticke=
rs,=20
but almost don't influence rotation descriptions. We need to define mask =
of=20
layers for the twist, and for that we must know only one thing - what is =
the=20
maximal number M of layers there is from the center to the surface (for a=
ll=20
axes) - not including central layer. For example, for 3^4 tesseract it wi=
ll be=20
1, and for 3^4 with diagonal cuttings x=B1y=B1z=B1w=3D{-2,0,2} (for x,y,z=
,w=3D{-1,1}) it=20
will be 2 (there are 3 layers orthogonal to (0,0,0,1) and 4 layers orthog=
onal=20
to (1,1,1,1) ). If such number M is defined, we enumerate layers by each =
axis=20
so that central layer (if it exists) has number M. If thare is no central=
=20
layer, M is skipped. For the example above layers parallel to cells will =
have=20
numbers 1,2,3 and layers in 0D direction (orthogonal to (1,1,1,1)) will b=
e=20
0,1,3,4.
This way we define the mask of the twist.

To define =
the=20
twist we need two more things - direction of 3D axis of twist and twistin=
g=20
angle. My guess is that 3D axis is always one of symmetry axes that is=20
perpendicular to the layer axis, so it is enumerated in our set. The prob=
lem=20
will be with the angle.

Some puzzles (such as 3x3x4x4, or alternat=
ed=20
puzzles like snub 24-cell) may have restricted set of twists enabled by t=
he=20
axes set. So we can't just write "turn on smallest possible angle clockwi=
se",=20
we need to define angle explicitly. I suggest to select some number D for=
=20
every axes set, that will be common divisor for all twist orders (not=20
necessarily the least) - 12 for simplex, hypercube or 24-cell, 60 for=20
120-cell, [n,k,2] for duoprism, include it in the set description and wri=
te=20
angles assuming D=3D360 deg.
So every twist will be described by 4=20
numbers:
- direction of main axis (orthogonal to the cutting plane)>-=20
direction of 3D axis (it's perpendicular to the main axis)
- rotation=
=20
angle
- layers mask

For example, 120-deg rotation of 3rd layer =
of=20
4^4 may have the form
A1:A2:4:8, where A1=3D(1,0,0,0) and A2=3D(0,1,-1=
,1)=20
(4=3D12/3, 8=3D2^3)

I don't want to include complete stickers mask=
in the=20
description (stickers order and description may be different for differen=
t=20
implementations), and don't see good way to define the starting situation=
. Of=20
course, we can find the description for every sticker It may include 4 cu=
tting=20
planes that give its vertex, and a mask that gives position of the sticke=
r=20
relative to these planes. But definition of the puzzle state is such term=
s=20
will be terrible. I afraid that we will be able to keep only possible=20
positions defined by the twists sequence.

All the other things - b=
ody=20
shape, coloring, position of cutting planes, mask/description of stickers=
, not=20
included in puzzle (and the shape of the remaining stickers), bandaging a=
nd so=20
on - it will be in the log header and its interpretation (=3D puzzle=20
description) is another story.

Andrey



------=_NextPart_000_0029_01CBD1CD.D072B3B0--




From: Roice Nelson <roice3@gmail.com>
Date: Tue, 22 Feb 2011 09:26:53 -0600
Subject: Re: [MC4D] Social dream



--001636c5ab092a3b91049ce09cb9
Content-Type: text/plain; charset=ISO-8859-1
Content-Transfer-Encoding: quoted-printable

I very much like what Andrey specified for the twist definition in future
log files.

The only thing I questioned while reading was whether it is necessary to
store the rotation angles in such a way that they depend on the puzzle. So
rather than storing 12/3=3D4 for a 120 degree rotation on the simplex, why =
not
simply store 3? This would make those values more readable across puzzles,
since any order-3 rotation would be saved the same. Maybe I am missing
another need there though.

Roice


On Mon, Feb 21, 2011 at 1:11 AM, Andrey wrote:

> Hi all,
> About piece finding and percentage of solving, there is a problem in the
> most puzzles: if puzzle has no unmoving center of the cell, you cannot sa=
y
> what is the proper color for this cell. So there is no way to say "what i=
s
> the place for this piece", "where this piece should go" and "how many
> pieces/stickers are in their places". Program can "guess" colors for face=
s
> (by majority of colors), but is may lead to strange situatons: you solve
> something like simplex, get one twisted corner piece, and can't solve it
> without reassigning colors to cells. But the program keeps telling you th=
at
> you are going from the correct solution, and number of solved pieces is
> decreasing (until you get enough stickers in their new cells)
> So I used alternative approach to piece-finding in MC7D. It works, but
> it's much less intuitive than "click in piece and see where it goes".
>
> As for the log files, my first idea is the following.
> Let we have some puzzle based on uniform polytope. Now we don't consider
> shape-transformers, so form of puzzle remains the same after each twist.
> Cutting hyperplanes are ortogonal to some axes (going through the center
> of the puzzle). These axes may contain centers of cells, 2D faces, middle=
s
> of edges and vertices of the puzzle, but it doesn't matter. What is
> important, the set of axes for the puzzle is a subset of symmetry/rotatio=
n
> axes of the puzzle body. There are not many symmetry sets in 4D:
> - symmetries of 5-cell (15 axes)
> - symmetries of bitruncated 5-cell (70 axes?)
> - symmetries of 8-cell (40 axes)
> - symmetries of 24-cell (120 axes)
> - symmetries of bitruncated 24-cell (624 axes?)
> - symmetries of 120-cell (1320 axes)
> - symmetries of duoprism [n]x[k] (n+k axes?)
> - symmetries of duoprism [n]x[n] (2*n+n^2 axes?)
>
> We can enumerate axes for every case in some agreed order.
>
> For every axis we have number and positions of cutting planes. They defin=
e
> number and connections of stickers, but almost don't influence rotation
> descriptions. We need to define mask of layers for the twist, and for tha=
t
> we must know only one thing - what is the maximal number M of layers ther=
e
> is from the center to the surface (for all axes) - not including central
> layer. For example, for 3^4 tesseract it will be 1, and for 3^4 with
> diagonal cuttings x=B1y=B1z=B1w=3D{-2,0,2} (for x,y,z,w=3D{-1,1}) it will=
be 2 (there
> are 3 layers orthogonal to (0,0,0,1) and 4 layers orthogonal to (1,1,1,1)=
).
> If such number M is defined, we enumerate layers by each axis so that
> central layer (if it exists) has number M. If thare is no central layer, =
M
> is skipped. For the example above layers parallel to cells will have numb=
ers
> 1,2,3 and layers in 0D direction (orthogonal to (1,1,1,1)) will be 0,1,3,=
4.
> This way we define the mask of the twist.
>
> To define the twist we need two more things - direction of 3D axis of twi=
st
> and twisting angle. My guess is that 3D axis is always one of symmetry ax=
es
> that is perpendicular to the layer axis, so it is enumerated in our set. =
The
> problem will be with the angle.
>
> Some puzzles (such as 3x3x4x4, or alternated puzzles like snub 24-cell) m=
ay
> have restricted set of twists enabled by the axes set. So we can't just
> write "turn on smallest possible angle clockwise", we need to define angl=
e
> explicitly. I suggest to select some number D for every axes set, that wi=
ll
> be common divisor for all twist orders (not necessarily the least) - 12 f=
or
> simplex, hypercube or 24-cell, 60 for 120-cell, [n,k,2] for duoprism,
> include it in the set description and write angles assuming D=3D360 deg.
> So every twist will be described by 4 numbers:
> - direction of main axis (orthogonal to the cutting plane)
> - direction of 3D axis (it's perpendicular to the main axis)
> - rotation angle
> - layers mask
>
> For example, 120-deg rotation of 3rd layer of 4^4 may have the form
> A1:A2:4:8, where A1=3D(1,0,0,0) and A2=3D(0,1,-1,1) (4=3D12/3, 8=3D2^3)
>
> I don't want to include complete stickers mask in the description (sticke=
rs
> order and description may be different for different implementations), an=
d
> don't see good way to define the starting situation. Of course, we can fi=
nd
> the description for every sticker It may include 4 cutting planes that gi=
ve
> its vertex, and a mask that gives position of the sticker relative to the=
se
> planes. But definition of the puzzle state is such terms will be terrible=
. I
> afraid that we will be able to keep only possible positions defined by th=
e
> twists sequence.
>
> All the other things - body shape, coloring, position of cutting planes,
> mask/description of stickers, not included in puzzle (and the shape of th=
e
> remaining stickers), bandaging and so on - it will be in the log header a=
nd
> its interpretation (=3D puzzle description) is another story.
>
> Andrey

--001636c5ab092a3b91049ce09cb9
Content-Type: text/html; charset=ISO-8859-1
Content-Transfer-Encoding: quoted-printable

I very much like what Andrey specified for the twist definition in future l=
og files.


The only thing I questioned while reading was =
whether it is necessary to store the rotation angles in such a way that the=
y depend on the puzzle. =A0So rather than storing 12/3=3D4 for a 120 degree=
rotation on the simplex, why not simply store 3? =A0This would make those =
values more readable across puzzles, since any order-3 rotation would be sa=
ved the same. =A0Maybe I am missing another need there though.



Roice


On M=
on, Feb 21, 2011 at 1:11 AM, Andrey <:andreyastrelin@yahoo.com" target=3D"_blank">andreyastrelin@yahoo.com&g=
t;
wrote:


x #ccc solid;padding-left:1ex">Hi all,

=A0About piece finding and percentage of solving, there is a problem in th=
e most puzzles: if puzzle has no unmoving center of the cell, you cannot sa=
y what is the proper color for this cell. So there is no way to say "w=
hat is the place for this piece", "where this piece should go&quo=
t; and "how many pieces/stickers are in their places". Program ca=
n "guess" colors for faces (by majority of colors), but is may le=
ad to strange situatons: you solve something like simplex, get one twisted =
corner piece, and can't solve it without reassigning colors to cells. B=
ut the program keeps telling you that you are going from the correct soluti=
on, and number of solved pieces is decreasing (until you get enough sticker=
s in their new cells)



=A0So I used alternative approach to piece-finding in MC7D. It works, but =
it's much less intuitive than "click in piece and see where it goe=
s".



=A0As for the log files, my first idea is the following.

=A0Let we have some puzzle based on uniform polytope. Now we don't con=
sider shape-transformers, so form of puzzle remains the same after each twi=
st.

=A0Cutting hyperplanes are ortogonal to some axes (going through the cente=
r of the puzzle). These axes may contain centers of cells, 2D faces, middle=
s of edges and vertices of the puzzle, but it doesn't matter. What is i=
mportant, the set of axes for the puzzle is a subset of symmetry/rotation a=
xes of the puzzle body. There are not many symmetry sets in 4D:



- symmetries of 5-cell (15 axes)

- symmetries of bitruncated 5-cell (70 axes?)

- symmetries of 8-cell (40 axes)

- symmetries of 24-cell (120 axes)

- symmetries of bitruncated 24-cell (624 axes?)

- symmetries of 120-cell (1320 axes)

- symmetries of duoprism [n]x[k] (n+k axes?)

- symmetries of duoprism [n]x[n] (2*n+n^2 axes?)



We can enumerate axes for every case in some agreed order.



For every axis we have number and positions of cutting planes. They define =
number and connections of stickers, but almost don't influence rotation=
descriptions. We need to define mask of layers for the twist, and for that=
we must know only one thing - what is the maximal number M of layers there=
is from the center to the surface (for all axes) - not including central l=
ayer. For example, for 3^4 tesseract it will be 1, and for 3^4 with diagona=
l cuttings x=B1y=B1z=B1w=3D{-2,0,2} (for x,y,z,w=3D{-1,1}) it will be 2 (th=
ere are 3 layers orthogonal to (0,0,0,1) and 4 layers orthogonal to (1,1,1,=
1) ). If such number M is defined, we enumerate layers by each axis so that=
central layer (if it exists) has number M. If thare is no central layer, M=
is skipped. For the example above layers parallel to cells will have numbe=
rs 1,2,3 and layers in 0D direction (orthogonal to (1,1,1,1)) will be 0,1,3=
,4.



This way we define the mask of the twist.



To define the twist we need two more things - direction of 3D axis of twist=
and twisting angle. My guess is that 3D axis is always one of symmetry axe=
s that is perpendicular to the layer axis, so it is enumerated in our set. =
The problem will be with the angle.





Some puzzles (such as 3x3x4x4, or alternated puzzles like snub 24-cell) may=
have restricted set of twists enabled by the axes set. So we can't jus=
t write "turn on smallest possible angle clockwise", we need to d=
efine angle explicitly. I suggest to select some number D for every axes se=
t, that will be common divisor for all twist orders (not necessarily the le=
ast) - 12 for simplex, hypercube or 24-cell, 60 for 120-cell, [n,k,2] for d=
uoprism, include it in the set description and write angles assuming D=3D36=
0 deg.



=A0So every twist will be described by 4 numbers:

- direction of main axis (orthogonal to the cutting plane)

- direction of 3D axis (it's perpendicular to the main axis)

- rotation angle

- layers mask



For example, 120-deg rotation of 3rd layer of 4^4 may have the form

A1:A2:4:8, where A1=3D(1,0,0,0) and A2=3D(0,1,-1,1) (4=3D12/3, 8=3D2^3)



I don't want to include complete stickers mask in the description (stic=
kers order and description may be different for different implementations),=
and don't see good way to define the starting situation. Of course, we=
can find the description for every sticker It may include 4 cutting planes=
that give its vertex, and a mask that gives position of the sticker relati=
ve to these planes. But definition of the puzzle state is such terms will b=
e terrible. I afraid that we will be able to keep only possible positions d=
efined by the twists sequence.





All the other things - body shape, coloring, position of cutting planes, ma=
sk/description of stickers, not included in puzzle (and the shape of the re=
maining stickers), bandaging and so on - it will be in the log header and i=
ts interpretation (=3D puzzle description) is another story.





Andrey


--001636c5ab092a3b91049ce09cb9--




From: "Andrey" <andreyastrelin@yahoo.com>
Date: Tue, 22 Feb 2011 16:24:28 -0000
Subject: Re: [MC4D] Social dream



Roice, thank you.
About angles: I suggest to keep them in the way where angle doesn't depen=
d on the puzzle. So that when you see the rotation angle value in the log f=
ile, you can find its value in degrees without knowing of the puzzle body.=
=20
For example, compare hyperboxes 4^4 and 3x3x4x4. If we have two axes (1,0=
,0,0) and (0,0,1,0) then 4^4 allows 90-deg twists in this direction, and fo=
r 3x3x4x4 only 180-deg twists are possible. In my notation 180-deg twists f=
or these two puzzles will have the same angle=3D6 (12/2).
Another example is something like alternated douprism [2n]x[2k] (it is no=
t included in uniform polychora list because some of its cells are non-regu=
lar tetrahedra). Rotation of its main cell (antiprism?) is possible only to=
360/n degrees. In the douprism [2n]x[2k] (with the same set of axes) rotat=
ions to 360/2n degrees are possible.
Also different programs may have different ideas about minimal rotation a=
ngle for some pair of axes in the set. If these values will be different th=
an there is more chance that programs will not understand each other's log.
Something like that.=20

Andrey


--- In 4D_Cubing@yahoogroups.com, Roice Nelson wrote:
>
> I very much like what Andrey specified for the twist definition in future
> log files.
>=20
> The only thing I questioned while reading was whether it is necessary to
> store the rotation angles in such a way that they depend on the puzzle. =
So
> rather than storing 12/3=3D4 for a 120 degree rotation on the simplex, wh=
y not
> simply store 3? This would make those values more readable across puzzle=
s,
> since any order-3 rotation would be saved the same. Maybe I am missing
> another need there though.
>=20
> Roice
>=20
>=20




From: Roice Nelson <roice3@gmail.com>
Date: Tue, 22 Feb 2011 10:53:33 -0600
Subject: Re: [MC4D] Social dream



--0015174c1c28214c56049ce1d28e
Content-Type: text/plain; charset=ISO-8859-1

On Tue, Feb 22, 2011 at 10:24 AM, Andrey wrote:

> About angles: I suggest to keep them in the way where angle doesn't depend
> on the puzzle. So that when you see the rotation angle value in the log
> file, you can find its value in degrees without knowing of the puzzle body.
> For example, compare hyperboxes 4^4 and 3x3x4x4. If we have two axes
> (1,0,0,0) and (0,0,1,0) then 4^4 allows 90-deg twists in this direction, and
> for 3x3x4x4 only 180-deg twists are possible. In my notation 180-deg twists
> for these two puzzles will have the same angle=6 (12/2).
>

But if I'm reading right, you are suggesting a 180-degree rotation on the
120-cell puzzle would be angle=30 (60/2). So the nature of the puzzle does
seem to affect how the same twist angle is recorded. It feels like it'd be
nicer if the recording of angles did not have this kind of dependency.

seeya,
Roice

--0015174c1c28214c56049ce1d28e
Content-Type: text/html; charset=ISO-8859-1
Content-Transfer-Encoding: quoted-printable

On Tue, Feb 22, 2011 at 10:24 AM, Andrey ir=3D"ltr"><andreyastrelin@y=
ahoo.com
>
wrote:

; PADDING-LEFT: 1ex" class=3D"gmail_quote">=A0About angles: I suggest to ke=
ep them in the way where angle doesn't depend on the puzzle. So that wh=
en you see the rotation angle value in the log file, you can find its value=
in degrees without knowing of the puzzle body.

=A0For example, compare hyperboxes 4^4 and 3x3x4x4. If we have two axes (1,=
0,0,0) and (0,0,1,0) then 4^4 allows 90-deg twists in this direction, and f=
or 3x3x4x4 only 180-deg twists are possible. In my notation 180-deg twists =
for these two puzzles will have the same angle=3D6 (12/2).


=A0

But if I'm reading right, you are suggesting a 180-degree rotation=
on the 120-cell puzzle would be angle=3D30 (60/2).=A0 So the nature of the=
puzzle does seem to affect how=A0the same twist angle=A0is recorded.=A0 It=
feels like it'd be nicer=A0if=A0the recording of=A0angles=A0did not ha=
ve this kind of dependency.


=A0
seeya,
Roice


--0015174c1c28214c56049ce1d28e--




From: "Andrey" <andreyastrelin@yahoo.com>
Date: Tue, 22 Feb 2011 18:56:39 -0000
Subject: Re: [MC4D] Social dream



Okay, let's write fractions of full turn: 1/2,2/3,2/5,37/100 etc. It's univ=
ersal (in 4D puzzles) and not a big problem for programs.

So twist record will look like 15:23:2/3:8 .

To enumerate axes of the set we can select some coordinate system (that is =
natural for tesseract, 24-cell and duoprisms, and we can select something f=
or 5-cell and 120-cell), get vectors of length 1 in directions of all axes,=
sort them in by w coordinate, then by z, by y and at last by x, and selec=
t the last (maximal) vector as 0, next as 1 and so on (for vectors greater =
than (0,0,0,0)). It may be difficult for human, but easy for the program.

Andrey

--- In 4D_Cubing@yahoogroups.com, "Andrey" wrote:
>
> I thought about usage of degrees (72, 120, 90,...) but it will not work f=
or douprisms. Actually I want to have rational number there, but it's more =
easy to write their common denominator is the head (near the set descriptio=
n) and show only numerators of the angle in all twists. We may write D=3D36=
0 for all puzzles other than douprisms.
> Or you want to write denominators only? Then again we'll need two records=
for 144-deg rotation... Not good when we can select format with one record=
for every twist of the cell/face/edge/vertex...
>=20
> Andrey
>=20
> >=20
> > But if I'm reading right, you are suggesting a 180-degree rotation on t=
he
> > 120-cell puzzle would be angle=3D30 (60/2). So the nature of the puzzl=
e does
> > seem to affect how the same twist angle is recorded. It feels like it'=
d be
> > nicer if the recording of angles did not have this kind of dependency.
> >=20
> > seeya,
> > Roice
> >
>




From: Melinda Green <melinda@superliminal.com>
Date: Tue, 22 Feb 2011 12:50:39 -0800
Subject: Re: [MC4D] Social dream



Andrey,

I'm glad that you are taking the lead on this subject because these log
files are the true model/document/heart of these puzzles. Various
programs that let users view and edit these files will come and go but
it would be truly wonderful if we can standardize on this core issue. I
like everything I've see so far in the discussion and I would like to
pose one additional question which is how well can we also support other
dimensional puzzles as well as flat and hyperbolic spaces? IOW, I would
like to know just how good or bad the fit will need to be in order to
support all of the puzzles that we have already created. I wouldn't want
to do it if it required ugly kludges but I'm sure that everyone would
agree that it would certainly be a truly lovely dream to retrofit our
existing puzzles to support a single "Grand Unified" twisty puzzle log
file format if it can be done in a natural way. Of course it would be
nice if the files ended up being human readable but that's not an
important goal because a simple read-only log file viewer can always be
written later. I would much rather have an unreadable format that covers
all twisty puzzles than to have several readable but incompatible formats.

-Melinda

On 2/22/2011 10:56 AM, Andrey wrote:
> Okay, let's write fractions of full turn: 1/2,2/3,2/5,37/100 etc. It's universal (in 4D puzzles) and not a big problem for programs.
>
> So twist record will look like 15:23:2/3:8 .
>
> To enumerate axes of the set we can select some coordinate system (that is natural for tesseract, 24-cell and duoprisms, and we can select something for 5-cell and 120-cell), get vectors of length 1 in directions of all axes, sort them in by w coordinate, then by z, by y and at last by x, and select the last (maximal) vector as 0, next as 1 and so on (for vectors greater than (0,0,0,0)). It may be difficult for human, but easy for the program.
>
> Andrey
>
> --- In 4D_Cubing@yahoogroups.com, "Andrey" wrote:
>> I thought about usage of degrees (72, 120, 90,...) but it will not work for douprisms. Actually I want to have rational number there, but it's more easy to write their common denominator is the head (near the set description) and show only numerators of the angle in all twists. We may write D=360 for all puzzles other than douprisms.
>> Or you want to write denominators only? Then again we'll need two records for 144-deg rotation... Not good when we can select format with one record for every twist of the cell/face/edge/vertex...
>>
>> Andrey
>>
>>> But if I'm reading right, you are suggesting a 180-degree rotation on the
>>> 120-cell puzzle would be angle=30 (60/2). So the nature of the puzzle does
>>> seem to affect how the same twist angle is recorded. It feels like it'd be
>>> nicer if the recording of angles did not have this kind of dependency.
>>>
>>> seeya,
>>> Roice
>>>
>
>
>
> ------------------------------------
>
> Yahoo! Groups Links
>
>
>
>




From: Roice Nelson <roice3@gmail.com>
Date: Tue, 22 Feb 2011 21:43:23 -0600
Subject: Re: [MC4D] Social dream



--0003255560ee1aff46049ceae643
Content-Type: text/plain; charset=ISO-8859-1

I like it :)

It would be good if we could come up with a way to specify the initial
orientation of the polytopes used to generate the axis set in a generic
manner, such that it didn't have to be considered for each polytope. I'd
even prefer this if the chosen coordinate systems were not very natural for
some of the shapes. Like you say, difficult for human, but easy for the
program.

I also like Melinda's suggestion to try to ensure everything is general if
possible. It feels like your thoughts extend perfectly well to 5D and other
dimensions. I'm not yet sure how to apply them to the hyperbolic puzzles of
MagicTile, but perhaps you already have thought about that and know how it
might go for MHT633?

Roice


On Tue, Feb 22, 2011 at 12:56 PM, Andrey wrote:

> Okay, let's write fractions of full turn: 1/2,2/3,2/5,37/100 etc. It's
> universal (in 4D puzzles) and not a big problem for programs.
>
> So twist record will look like 15:23:2/3:8 .
>
> To enumerate axes of the set we can select some coordinate system (that is
> natural for tesseract, 24-cell and duoprisms, and we can select something
> for 5-cell and 120-cell), get vectors of length 1 in directions of all axes,
> sort them in by w coordinate, then by z, by y and at last by x, and select
> the last (maximal) vector as 0, next as 1 and so on (for vectors greater
> than (0,0,0,0)). It may be difficult for human, but easy for the program.
>
> Andrey
>
> --- In 4D_Cubing@yahoogroups.com, "Andrey" wrote:
> >
> > I thought about usage of degrees (72, 120, 90,...) but it will not work
> for douprisms. Actually I want to have rational number there, but it's more
> easy to write their common denominator is the head (near the set
> description) and show only numerators of the angle in all twists. We may
> write D=360 for all puzzles other than douprisms.
> > Or you want to write denominators only? Then again we'll need two records
> for 144-deg rotation... Not good when we can select format with one record
> for every twist of the cell/face/edge/vertex...
> >
> > Andrey
> >
> > >
> > > But if I'm reading right, you are suggesting a 180-degree rotation on
> the
> > > 120-cell puzzle would be angle=30 (60/2). So the nature of the puzzle
> does
> > > seem to affect how the same twist angle is recorded. It feels like
> it'd be
> > > nicer if the recording of angles did not have this kind of dependency.
> > >
> > > seeya,
> > > Roice
> > >
> >
>
>
>
>
> ------------------------------------
>
> Yahoo! Groups Links
>
>
>
>

--0003255560ee1aff46049ceae643
Content-Type: text/html; charset=ISO-8859-1
Content-Transfer-Encoding: quoted-printable

I like it :)

=A0

It would be good if we could come up with a way to specify the initial=
orientation of the polytopes used to generate the axis set in a generic ma=
nner, such that it didn't have to be considered for each polytope.=A0 I=
'd even prefer this if the chosen coordinate systems were not very natu=
ral for some of the shapes.=A0 Like you say, difficult for human, but easy =
for the program.



=A0

I also like Melinda's suggestion to try to ensure everything is ge=
neral if possible. =A0It feels like your thoughts extend perfectly well to =
5D and other dimensions. =A0I'm not yet sure how to apply them to the h=
yperbolic puzzles of MagicTile, but perhaps you already have thought about =
that and know how it might go for MHT633?


Roice



On Tue, Feb 22, 2011 at 12:56 PM, Andrey ir=3D"ltr"><">andreyastrelin@yahoo.com> wrote:

dding-left:1ex" class=3D"gmail_quote">Okay, let's write fractions of fu=
ll turn: 1/2,2/3,2/5,37/100 etc. It's universal (in 4D puzzles) and not=
a big problem for programs.



So twist record will look like 15:23:2/3:8 .

To enumerate axes o=
f the set we can select some coordinate system (that is natural for tessera=
ct, 24-cell and duoprisms, and we can select something for 5-cell and 120-c=
ell), get vectors of length 1 in directions of all axes, sort them in by w =
coordinate, then by z, by y and =A0at last by x, and select the last (maxim=
al) vector as 0, next as 1 and so on (for vectors greater than (0,0,0,0)). =
It may be difficult for human, but easy for the program.



Andrey




--- In nk">4D_Cubing@yahoogroups.com, "Andrey" <andreyastrelin@..=
.> wrote:
>
> I thought about usage of degrees (72, 120, 90,=
...) but it will not work for douprisms. Actually I want to have rational n=
umber there, but it's more easy to write their common denominator is th=
e head (near the set description) and show only numerators of the angle in =
all twists. We may write D=3D360 for all puzzles other than douprisms.


> Or you want to write denominators only? Then again we'll need two =
records for 144-deg rotation... Not good when we can select format with one=
record for every twist of the cell/face/edge/vertex...
>
> And=
rey


>
> >
> > But if I'm reading right, you are sugges=
ting a 180-degree rotation on the
> > 120-cell puzzle would be ang=
le=3D30 (60/2). =A0So the nature of the puzzle does
> > seem to af=
fect how the same twist angle is recorded. =A0It feels like it'd be


> > nicer if the recording of angles did not have this kind of depend=
ency.
> >
> > seeya,
> > Roice
> >
&=
gt;




------------------------------------

Yahoo! G=
roups Links



<*> To visit your group on the web, go to:
=A0 =A0ttp://groups.yahoo.com/group/4D_Cubing/" target=3D"_blank">http://groups.ya=
hoo.com/group/4D_Cubing/


<*> Your email settings:
=A0 =
=A0Individual Email | Traditional



<*> To change settings online go to:
=A0 =A0groups.yahoo.com/group/4D_Cubing/join" target=3D"_blank">http://groups.yaho=
o.com/group/4D_Cubing/join

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<*&=
gt; To change settings via email:


=A0 =A0">4D_Cubing-digest@yahoogroups.com
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hoogroups.com




<*> To unsubscribe from this group, send an email to:
=A0 =A0<=
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<*> Your use of Yahoo=
! Groups is subject to:


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://docs.yahoo.com/info/terms/


>

--0003255560ee1aff46049ceae643--




From: "Andrey" <andreyastrelin@yahoo.com>
Date: Wed, 23 Feb 2011 07:31:13 -0000
Subject: Re: [MC4D] Social dream



Roice,
We don't need to calculate axis set for each polytope. The list that I pr=
esented in the first message is complete for non-prismatic bodies. For pris=
ms there will be 5 or so more axes sets, but we can include them in log str=
ucture description with the coordinate system (and axis ordering) for every=
set.
Initial camera position may be different for different bodies, but I thin=
k that it'll be enough to keep camera position in the program-specific sect=
ion of log (that will be read by the program that created log file and igno=
red by other programs).
Twist definition by two axes is good only for 4D polytopes with axes pass=
ing through the body center. For 5D and more we shold return to the restric=
ted set of elementary twists (and I'm not sure that 3 axes will give defini=
tion of the twist - take for example 5D simplex with its 3-cycles of cells.=
What axis goes where?). For flats we should have separate enumeration of r=
otation centers (and use center instead of the first axis) - not a big deal=
, log structure will be almost the same, but... there is infinite number of=
centers and we must describe periodic pattern that gives finite centers se=
t (and enumeration will depend on this pattern). And in hyperbolic spaces w=
e have no vectors at all - so there will be something very different for st=
icker-free twist definitions.

Andrey


--- In 4D_Cubing@yahoogroups.com, Roice Nelson wrote:
>
> I like it :)
>=20
> It would be good if we could come up with a way to specify the initial
> orientation of the polytopes used to generate the axis set in a generic
> manner, such that it didn't have to be considered for each polytope. I'd
> even prefer this if the chosen coordinate systems were not very natural f=
or
> some of the shapes. Like you say, difficult for human, but easy for the
> program.
>=20
> I also like Melinda's suggestion to try to ensure everything is general i=
f
> possible. It feels like your thoughts extend perfectly well to 5D and ot=
her
> dimensions. I'm not yet sure how to apply them to the hyperbolic puzzles=
of
> MagicTile, but perhaps you already have thought about that and know how i=
t
> might go for MHT633?
>=20
> Roice
>=20
>=20
> On Tue, Feb 22, 2011 at 12:56 PM, Andrey wrote:
>=20
> > Okay, let's write fractions of full turn: 1/2,2/3,2/5,37/100 etc. It's
> > universal (in 4D puzzles) and not a big problem for programs.
> >
> > So twist record will look like 15:23:2/3:8 .
> >
> > To enumerate axes of the set we can select some coordinate system (that=
is
> > natural for tesseract, 24-cell and duoprisms, and we can select somethi=
ng
> > for 5-cell and 120-cell), get vectors of length 1 in directions of all =
axes,
> > sort them in by w coordinate, then by z, by y and at last by x, and se=
lect
> > the last (maximal) vector as 0, next as 1 and so on (for vectors greate=
r
> > than (0,0,0,0)). It may be difficult for human, but easy for the progra=
m.
> >
> > Andrey
> >
> > --- In 4D_Cubing@yahoogroups.com, "Andrey" wrote:
> > >
> > > I thought about usage of degrees (72, 120, 90,...) but it will not wo=
rk
> > for douprisms. Actually I want to have rational number there, but it's =
more
> > easy to write their common denominator is the head (near the set
> > description) and show only numerators of the angle in all twists. We ma=
y
> > write D=3D360 for all puzzles other than douprisms.
> > > Or you want to write denominators only? Then again we'll need two rec=
ords
> > for 144-deg rotation... Not good when we can select format with one rec=
ord
> > for every twist of the cell/face/edge/vertex...
> > >
> > > Andrey
> > >
> > > >
> > > > But if I'm reading right, you are suggesting a 180-degree rotation =
on
> > the
> > > > 120-cell puzzle would be angle=3D30 (60/2). So the nature of the p=
uzzle
> > does
> > > > seem to affect how the same twist angle is recorded. It feels like
> > it'd be
> > > > nicer if the recording of angles did not have this kind of dependen=
cy.
> > > >
> > > > seeya,
> > > > Roice
> > > >
> > >
> >
> >
> >
> >
> > ------------------------------------
> >
> > Yahoo! Groups Links
> >
> >
> >
> >
>




From: "Andrew Gould" <agould@uwm.edu>
Date: Fri, 25 Feb 2011 17:09:29 -0600
Subject: RE: [MC4D] Social dream



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boundary="----=_NextPart_001_001E_01CBD50E.C39F8160"

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charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

I'm seeing 46 rotational planes for the tesseract (6 planes for 90-degree
rotations, 24 for 180-degree, 16 for 120-degree), now I'm trying to
translate into Andrey's 40 axes--I got confused.

=20

I'm keeping my so-called "2D twists" in mind. They seem to use the same
axes/rotational planes that are already used.=20=20

http://groups.yahoo.com/group/4D_Cubing/photos/album/1774759718/pic/list

=20

The deal in 5D is that you can twist 4D slices, 3D slices, or 2D
slices...but again I'm seeing that they all get twisted about
axes/rotational planes that are already used for twisting 4D slices.=20=20

=20

--

Andy

=20

=20

From: 4D_Cubing@yahoogroups.com [mailto:4D_Cubing@yahoogroups.com] On Behal=
f
Of Andrey
Sent: Monday, February 21, 2011 1:12
To: 4D_Cubing@yahoogroups.com
Subject: Re: [MC4D] Social dream

=20

=20=20

Hi all,
About piece finding and percentage of solving, there is a problem in the
most puzzles: if puzzle has no unmoving center of the cell, you cannot say
what is the proper color for this cell. So there is no way to say "what is
the place for this piece", "where this piece should go" and "how many
pieces/stickers are in their places". Program can "guess" colors for faces
(by majority of colors), but is may lead to strange situatons: you solve
something like simplex, get one twisted corner piece, and can't solve it
without reassigning colors to cells. But the program keeps telling you that
you are going from the correct solution, and number of solved pieces is
decreasing (until you get enough stickers in their new cells)=20
So I used alternative approach to piece-finding in MC7D. It works, but it's
much less intuitive than "click in piece and see where it goes".

As for the log files, my first idea is the following.
Let we have some puzzle based on uniform polytope. Now we don't consider
shape-transformers, so form of puzzle remains the same after each twist.
Cutting hyperplanes are ortogonal to some axes (going through the center of
the puzzle). These axes may contain centers of cells, 2D faces, middles of
edges and vertices of the puzzle, but it doesn't matter. What is important,
the set of axes for the puzzle is a subset of symmetry/rotation axes of the
puzzle body. There are not many symmetry sets in 4D:
- symmetries of 5-cell (15 axes)
- symmetries of bitruncated 5-cell (70 axes?)
- symmetries of 8-cell (40 axes)
- symmetries of 24-cell (120 axes)
- symmetries of bitruncated 24-cell (624 axes?)
- symmetries of 120-cell (1320 axes)
- symmetries of duoprism [n]x[k] (n+k axes?)
- symmetries of duoprism [n]x[n] (2*n+n^2 axes?)

We can enumerate axes for every case in some agreed order.

For every axis we have number and positions of cutting planes. They define
number and connections of stickers, but almost don't influence rotation
descriptions. We need to define mask of layers for the twist, and for that
we must know only one thing - what is the maximal number M of layers there
is from the center to the surface (for all axes) - not including central
layer. For example, for 3^4 tesseract it will be 1, and for 3^4 with
diagonal cuttings x=B1y=B1z=B1w=3D{-2,0,2} (for x,y,z,w=3D{-1,1}) it will b=
e 2 (there
are 3 layers orthogonal to (0,0,0,1) and 4 layers orthogonal to (1,1,1,1) )=
.
If such number M is defined, we enumerate layers by each axis so that
central layer (if it exists) has number M. If thare is no central layer, M
is skipped. For the example above layers parallel to cells will have number=
s
1,2,3 and layers in 0D direction (orthogonal to (1,1,1,1)) will be 0,1,3,4.=
=20
This way we define the mask of the twist.=20

To define the twist we need two more things - direction of 3D axis of twist
and twisting angle. My guess is that 3D axis is always one of symmetry axes
that is perpendicular to the layer axis, so it is enumerated in our set. Th=
e
problem will be with the angle.

Some puzzles (such as 3x3x4x4, or alternated puzzles like snub 24-cell) may
have restricted set of twists enabled by the axes set. So we can't just
write "turn on smallest possible angle clockwise", we need to define angle
explicitly. I suggest to select some number D for every axes set, that will
be common divisor for all twist orders (not necessarily the least) - 12 for
simplex, hypercube or 24-cell, 60 for 120-cell, [n,k,2] for duoprism,
include it in the set description and write angles assuming D=3D360 deg.
So every twist will be described by 4 numbers:
- direction of main axis (orthogonal to the cutting plane)
- direction of 3D axis (it's perpendicular to the main axis)
- rotation angle
- layers mask

For example, 120-deg rotation of 3rd layer of 4^4 may have the form
A1:A2:4:8, where A1=3D(1,0,0,0) and A2=3D(0,1,-1,1) (4=3D12/3, 8=3D2^3)

I don't want to include complete stickers mask in the description (stickers
order and description may be different for different implementations), and
don't see good way to define the starting situation. Of course, we can find
the description for every sticker It may include 4 cutting planes that give
its vertex, and a mask that gives position of the sticker relative to these
planes. But definition of the puzzle state is such terms will be terrible. =
I
afraid that we will be able to keep only possible positions defined by the
twists sequence.

All the other things - body shape, coloring, position of cutting planes,
mask/description of stickers, not included in puzzle (and the shape of the
remaining stickers), bandaging and so on - it will be in the log header and
its interpretation (=3D puzzle description) is another story.

Andrey




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oNormal>color:#1F497D'>I'm seeing 46 rotational planes for the tesseract (6 planes =
for 90-degree rotations, 24 for 180-degree, 16 for 120-degree), now I'm try=
ing to translate into Andrey's 40 axes--I got confused.
p>

","sans-serif";color:#1F497D'> 

mal>r:#1F497D'>I'm keeping my so-called "2D twists" in mind.=A0 They =
seem to use the same axes/rotational planes that are already used.=A0 =

family:"Calibri","sans-serif";color:#1F497D'>http://groups.yahoo.com/group/=
4D_Cubing/photos/album/1774759718/pic/list

MsoNormal>";color:#1F497D'> 

le=3D'font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Th=
e deal in 5D is that you can twist 4D slices, 3D slices, or 2D slices...but=
again I'm seeing that they all get twisted about axes/rotational planes th=
at are already used for twisting 4D slices.=A0

ss=3DMsoNormal>serif";color:#1F497D'> 

n style=3D'font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497=
D'>--

.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Andyn>

ibri","sans-serif";color:#1F497D'> 

oNormal>color:#1F497D'> 

order-top:solid #B5C4DF 1.0pt;padding:3.0pt 0in 0in 0in'>

al>Fr=
om:
rif"'> 4D_Cubing@yahoogroups.com [mailto:4D_Cubing@yahoogroups.com] On B=
ehalf Of
Andrey
Sent: Monday, February 21, 2011 1:12
To=
:
4D_Cubing@yahoogroups.com
Subject: Re: [MC4D] Social dream<=
o:p>

 

=

 

grp-msg>

Hi all,
Ab=
out piece finding and percentage of solving, there is a problem in the most=
puzzles: if puzzle has no unmoving center of the cell, you cannot say what=
is the proper color for this cell. So there is no way to say "what is=
the place for this piece", "where this piece should go" and=
"how many pieces/stickers are in their places". Program can &quo=
t;guess" colors for faces (by majority of colors), but is may lead to =
strange situatons: you solve something like simplex, get one twisted corner=
piece, and can't solve it without reassigning colors to cells. But the pro=
gram keeps telling you that you are going from the correct solution, and nu=
mber of solved pieces is decreasing (until you get enough stickers in their=
new cells)
So I used alternative approach to piece-finding in MC7D. It=
works, but it's much less intuitive than "click in piece and see wher=
e it goes".

As for the log files, my first idea is the followin=
g.
Let we have some puzzle based on uniform polytope. Now we don't consi=
der shape-transformers, so form of puzzle remains the same after each twist=
.
Cutting hyperplanes are ortogonal to some axes (going through the cent=
er of the puzzle). These axes may contain centers of cells, 2D faces, middl=
es of edges and vertices of the puzzle, but it doesn't matter. What is impo=
rtant, the set of axes for the puzzle is a subset of symmetry/rotation axes=
of the puzzle body. There are not many symmetry sets in 4D:
- symmetrie=
s of 5-cell (15 axes)
- symmetries of bitruncated 5-cell (70 axes?)
-=
symmetries of 8-cell (40 axes)
- symmetries of 24-cell (120 axes)
- =
symmetries of bitruncated 24-cell (624 axes?)
- symmetries of 120-cell (=
1320 axes)
- symmetries of duoprism [n]x[k] (n+k axes?)
- symmetries =
of duoprism [n]x[n] (2*n+n^2 axes?)

We can enumerate axes for every =
case in some agreed order.

For every axis we have number and positio=
ns of cutting planes. They define number and connections of stickers, but a=
lmost don't influence rotation descriptions. We need to define mask of laye=
rs for the twist, and for that we must know only one thing - what is the ma=
ximal number M of layers there is from the center to the surface (for all a=
xes) - not including central layer. For example, for 3^4 tesseract it will =
be 1, and for 3^4 with diagonal cuttings x=B1y=B1z=B1w=3D{-2,0,2} (for x,y,=
z,w=3D{-1,1}) it will be 2 (there are 3 layers orthogonal to (0,0,0,1) and =
4 layers orthogonal to (1,1,1,1) ). If such number M is defined, we enumera=
te layers by each axis so that central layer (if it exists) has number M. I=
f thare is no central layer, M is skipped. For the example above layers par=
allel to cells will have numbers 1,2,3 and layers in 0D direction (orthogon=
al to (1,1,1,1)) will be 0,1,3,4.
This way we define the mask of the tw=
ist.

To define the twist we need two more things - direction of 3D =
axis of twist and twisting angle. My guess is that 3D axis is always one of=
symmetry axes that is perpendicular to the layer axis, so it is enumerated=
in our set. The problem will be with the angle.

Some puzzles (such =
as 3x3x4x4, or alternated puzzles like snub 24-cell) may have restricted se=
t of twists enabled by the axes set. So we can't just write "turn on s=
mallest possible angle clockwise", we need to define angle explicitly.=
I suggest to select some number D for every axes set, that will be common =
divisor for all twist orders (not necessarily the least) - 12 for simplex, =
hypercube or 24-cell, 60 for 120-cell, [n,k,2] for duoprism, include it in =
the set description and write angles assuming D=3D360 deg.
So every twis=
t will be described by 4 numbers:
- direction of main axis (orthogonal t=
o the cutting plane)
- direction of 3D axis (it's perpendicular to the m=
ain axis)
- rotation angle
- layers mask

For example, 120-deg =
rotation of 3rd layer of 4^4 may have the form
A1:A2:4:8, where A1=3D(1,=
0,0,0) and A2=3D(0,1,-1,1) (4=3D12/3, 8=3D2^3)

I don't want to inclu=
de complete stickers mask in the description (stickers order and descriptio=
n may be different for different implementations), and don't see good way t=
o define the starting situation. Of course, we can find the description for=
every sticker It may include 4 cutting planes that give its vertex, and a =
mask that gives position of the sticker relative to these planes. But defin=
ition of the puzzle state is such terms will be terrible. I afraid that we =
will be able to keep only possible positions defined by the twists sequence=
.

All the other things - body shape, coloring, position of cutting p=
lanes, mask/description of stickers, not included in puzzle (and the shape =
of the remaining stickers), bandaging and so on - it will be in the log hea=
der and its interpretation (=3D puzzle description) is another story.
r>Andrey

:white'>


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From: Roice Nelson <roice3@gmail.com>
Date: Sat, 26 Feb 2011 15:15:19 -0600
Subject: Re: [MC4D] Social dream



--001636c5a83f9e8f1b049d35f190
Content-Type: text/plain; charset=ISO-8859-1

Hi Andy,

I think the calculation for count of symmetry axes for the tesseract goes
like this:

count = ( 8 + 24 + 32 + 16 ) / 2 = 40

8 cells
24 faces
32 edges
16 vertices

You divide by two because each axis gets counted twice in the sum, due to
antipodal elements.

Cheers,
Roice


On Fri, Feb 25, 2011 at 5:09 PM, Andrew Gould wrote:

>
>
> I'm seeing 46 rotational planes for the tesseract (6 planes for 90-degree
> rotations, 24 for 180-degree, 16 for 120-degree), now I'm trying to
> translate into Andrey's 40 axes--I got confused.
>
>
>
> I'm keeping my so-called "2D twists" in mind. They seem to use the same
> axes/rotational planes that are already used.
>
> http://groups.yahoo.com/group/4D_Cubing/photos/album/1774759718/pic/list
>
>
>
> The deal in 5D is that you can twist 4D slices, 3D slices, or 2D
> slices...but again I'm seeing that they all get twisted about
> axes/rotational planes that are already used for twisting 4D slices.
>
>
>
> --
>
> Andy
>

--001636c5a83f9e8f1b049d35f190
Content-Type: text/html; charset=ISO-8859-1
Content-Transfer-Encoding: quoted-printable

Hi Andy,

I think the calculation for count of=
symmetry axes for the tesseract goes like this:

c=
ount =3D ( 8 + 24 + 32 + 16 ) / 2 =3D 40

8 cellsdiv>

24 faces
32 edges
16 vertices

=
You divide by two because each axis gets counted twice in the sum, due=
to antipodal elements.

Cheers,
Roiceiv>



On Fri, Feb 25, 2011 at 5:09 PM, A=
ndrew Gould <=3D"_blank">agould@uwm.edu> wrote:
ail_quote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-le=
ft:1ex">








=20=20=20=20=20=20=20=20












=
I'm seeing 46 rotational planes for the tesseract (6 planes for 90-degr=
ee rotations, 24 for 180-degree, 16 for 120-degree), now I'm trying to =
translate into Andrey's 40 axes--I got confused.



=A0span>

7D">I'm keeping my so-called "2D twists" in mind.=A0 They see=
m to use the same axes/rotational planes that are already used.=A0
<=
/p>

ef=3D"http://groups.yahoo.com/group/4D_Cubing/photos/album/1774759718/pic/l=
ist" target=3D"_blank">http://groups.yahoo.com/group/4D_Cubing/photos/album=
/1774759718/pic/list



=A0span>

7D">The deal in 5D is that you can twist 4D slices, 3D slices, or 2D slices=
...but again I'm seeing that they all get twisted about axes/rotational=
planes that are already used for twisting 4D slices.=A0



=A0span>

7D">--

or:#1F497D">Andy





--001636c5a83f9e8f1b049d35f190--




From: "Andrey" <andreyastrelin@yahoo.com>
Date: Mon, 28 Feb 2011 10:32:28 -0000
Subject: Re: [MC4D] Social dream



Hi Andy,
I see 12 more rotational planes: they have fixed bivectors (1,1,0,0)x(0,0=
,1,1) with sign changes and coordinate permutations.=20
These planes can't be used in 3D-centered twists (because bi-axis doesn't=
contain coordinate vectors), but there is a couple of 180-deg twists with =
them:
2D-centered twist is here: ing/photos/album/1184359940/pic/527704145/view" />
and 0D-centered is here: g/photos/album/1184359940/pic/579107863/view" />

So if you have some rotation in 4D around the plane [P,Q] where P and Q are=
some vectors, you may select any cutting plane perpendicular to vector R f=
rom [P,Q] and then rotate the slice around some other vector R1 from [P,Q].

For example, in the most simple situation when bi-axis is (1,0,0,0)x(0,1,0,=
0), one can use it to rotate any of 4 dufferent 3D cells (R=3D(1,0,0,0) or =
(0,1,0,0)), or any of 4 2D ridges (R=3D(1,1,0,0) or R=3D(1,-1,0,0)).

When I wrote my description of twist, I thought that if we select vector R1=
perpendicular to R, then it will be an axis of the figure. But now I see t=
hat it's wrong: if we take R=3D(1,1,1,1) (0D-centered twist) and perform 12=
0-degree rotation, then actual axis R1 will be something like (-3,1,1,1) th=
at is not any axis of the tesseract. Of course, I can write in log that R1=
=3D(0,1,1,1) or (1,0,0,0) (so that [R,R1] gives the rotation bi-axis), but =
such selection will be arbitrary, not canonical, and I'm not sure that the =
rotational bi-axis will always contain two axes of the figure.

It looks like we should enumerate all rotational planes as well as axes, an=
d use orthogonal pairs (axis,plane) in the log file.

This method will work for all finite puzzles where twists can be defined in=
2D way (with D-2 dimensional multy-axis), but there will be a lot of exter=
nal data for the axes set definitions (list of axes, and list of planes - a=
nd there are some infinite families of sets...) So format will be not as el=
egant as it supposed to be.=20

For 3^5 there is a restricted set with only 5 axes and 10 rotational planes=
- and only 30 axis/plane pairs may appear in log. For 3^7 there are 7 axes=
and 21 planes (105 possible combinations) an for 5D simplex we have 6 axes=
and 20 planes (or 10? not sure) that give us 120 deg-twists of faces.


Andrey

--- In 4D_Cubing@yahoogroups.com, "Andrew Gould" wrote:
>
> I'm seeing 46 rotational planes for the tesseract (6 planes for 90-degree
> rotations, 24 for 180-degree, 16 for 120-degree), now I'm trying to
> translate into Andrey's 40 axes--I got confused.
>=20
>=20=20
>=20
> I'm keeping my so-called "2D twists" in mind. They seem to use the same
> axes/rotational planes that are already used.=20=20
>=20
> http://groups.yahoo.com/group/4D_Cubing/photos/album/1774759718/pic/list
>=20
>=20=20
>=20
> The deal in 5D is that you can twist 4D slices, 3D slices, or 2D
> slices...but again I'm seeing that they all get twisted about
> axes/rotational planes that are already used for twisting 4D slices.=20=20
>=20
>=20=20
>=20
> --
>=20
> Andy
>=20
>=20=20
>=20
>=20=20
>=20
> From: 4D_Cubing@yahoogroups.com [mailto:4D_Cubing@yahoogroups.com] On Beh=
alf
> Of Andrey
> Sent: Monday, February 21, 2011 1:12
> To: 4D_Cubing@yahoogroups.com
> Subject: Re: [MC4D] Social dream
>=20
>=20=20
>=20
>=20=20=20
>=20
> Hi all,
> About piece finding and percentage of solving, there is a problem in the
> most puzzles: if puzzle has no unmoving center of the cell, you cannot sa=
y
> what is the proper color for this cell. So there is no way to say "what i=
s
> the place for this piece", "where this piece should go" and "how many
> pieces/stickers are in their places". Program can "guess" colors for face=
s
> (by majority of colors), but is may lead to strange situatons: you solve
> something like simplex, get one twisted corner piece, and can't solve it
> without reassigning colors to cells. But the program keeps telling you th=
at
> you are going from the correct solution, and number of solved pieces is
> decreasing (until you get enough stickers in their new cells)=20
> So I used alternative approach to piece-finding in MC7D. It works, but it=
's
> much less intuitive than "click in piece and see where it goes".
>=20
> As for the log files, my first idea is the following.
> Let we have some puzzle based on uniform polytope. Now we don't consider
> shape-transformers, so form of puzzle remains the same after each twist.
> Cutting hyperplanes are ortogonal to some axes (going through the center =
of
> the puzzle). These axes may contain centers of cells, 2D faces, middles o=
f
> edges and vertices of the puzzle, but it doesn't matter. What is importan=
t,
> the set of axes for the puzzle is a subset of symmetry/rotation axes of t=
he
> puzzle body. There are not many symmetry sets in 4D:
> - symmetries of 5-cell (15 axes)
> - symmetries of bitruncated 5-cell (70 axes?)
> - symmetries of 8-cell (40 axes)
> - symmetries of 24-cell (120 axes)
> - symmetries of bitruncated 24-cell (624 axes?)
> - symmetries of 120-cell (1320 axes)
> - symmetries of duoprism [n]x[k] (n+k axes?)
> - symmetries of duoprism [n]x[n] (2*n+n^2 axes?)
>=20
> We can enumerate axes for every case in some agreed order.
>=20
> For every axis we have number and positions of cutting planes. They defin=
e
> number and connections of stickers, but almost don't influence rotation
> descriptions. We need to define mask of layers for the twist, and for tha=
t
> we must know only one thing - what is the maximal number M of layers ther=
e
> is from the center to the surface (for all axes) - not including central
> layer. For example, for 3^4 tesseract it will be 1, and for 3^4 with
> diagonal cuttings x=B1y=B1z=B1w=3D{-2,0,2} (for x,y,z,w=3D{-1,1}) it will=
be 2 (there
> are 3 layers orthogonal to (0,0,0,1) and 4 layers orthogonal to (1,1,1,1)=
).
> If such number M is defined, we enumerate layers by each axis so that
> central layer (if it exists) has number M. If thare is no central layer, =
M
> is skipped. For the example above layers parallel to cells will have numb=
ers
> 1,2,3 and layers in 0D direction (orthogonal to (1,1,1,1)) will be 0,1,3,=
4.=20
> This way we define the mask of the twist.=20
>=20
> To define the twist we need two more things - direction of 3D axis of twi=
st
> and twisting angle. My guess is that 3D axis is always one of symmetry ax=
es
> that is perpendicular to the layer axis, so it is enumerated in our set. =
The
> problem will be with the angle.
>=20
> Some puzzles (such as 3x3x4x4, or alternated puzzles like snub 24-cell) m=
ay
> have restricted set of twists enabled by the axes set. So we can't just
> write "turn on smallest possible angle clockwise", we need to define angl=
e
> explicitly. I suggest to select some number D for every axes set, that wi=
ll
> be common divisor for all twist orders (not necessarily the least) - 12 f=
or
> simplex, hypercube or 24-cell, 60 for 120-cell, [n,k,2] for duoprism,
> include it in the set description and write angles assuming D=3D360 deg.
> So every twist will be described by 4 numbers:
> - direction of main axis (orthogonal to the cutting plane)
> - direction of 3D axis (it's perpendicular to the main axis)
> - rotation angle
> - layers mask
>=20
> For example, 120-deg rotation of 3rd layer of 4^4 may have the form
> A1:A2:4:8, where A1=3D(1,0,0,0) and A2=3D(0,1,-1,1) (4=3D12/3, 8=3D2^3)
>=20
> I don't want to include complete stickers mask in the description (sticke=
rs
> order and description may be different for different implementations), an=
d
> don't see good way to define the starting situation. Of course, we can fi=
nd
> the description for every sticker It may include 4 cutting planes that gi=
ve
> its vertex, and a mask that gives position of the sticker relative to the=
se
> planes. But definition of the puzzle state is such terms will be terrible=
. I
> afraid that we will be able to keep only possible positions defined by th=
e
> twists sequence.
>=20
> All the other things - body shape, coloring, position of cutting planes,
> mask/description of stickers, not included in puzzle (and the shape of th=
e
> remaining stickers), bandaging and so on - it will be in the log header a=
nd
> its interpretation (=3D puzzle description) is another story.
>=20
> Andrey
>




From: Roice Nelson <roice3@gmail.com>
Date: Mon, 28 Feb 2011 18:18:51 -0600
Subject: Re: [MC4D] Social dream



--0016e6da9343b0f898049d60bd9a
Content-Type: text/plain; charset=ISO-8859-1

Hi Andy/Andrey,

I clearly missed the issue Andy raised earlier, so apologies for my
previous email in this thread, which probably appeared as both obvious and a
bit of a non sequitur.

Anyway, I can't help myself from feeling like this is getting quite
complicated, which feels a bit unfortunate. I do like that the new
suggestion looks to handle the 5D case now, but I found my mind trying to
find a way around enumerating the full set of rotational planes in the
file (especially in the 4D case). Those will all have to be generated and
ordered in a specified manner, like the axes. (This left me wondering if it
would be simpler to specify how to algorithmically generate/order stickers.)

I am uncertain about something else now too (in the 4D case). Early on,
Andrey wrote:


> For every axis we have number and positions of cutting planes.


The spaces orthogonal to the 4D symmetry axes are 3D. So it seems a cutting
plane position will need to contain orientation information as well (not
just a single number of how deep the cut is on the axis). Is that right?
If so, maybe the rotational plane and cutting plane data both reference the
same underlying set?

Best,
Roice


On Mon, Feb 28, 2011 at 4:32 AM, Andrey wrote:

> Hi Andy,
> I see 12 more rotational planes: they have fixed bivectors
> (1,1,0,0)x(0,0,1,1) with sign changes and coordinate permutations.
> These planes can't be used in 3D-centered twists (because bi-axis doesn't
> contain coordinate vectors), but there is a couple of 180-deg twists with
> them:
> 2D-centered twist is here: > />
> and 0D-centered is here: > />
>
> So if you have some rotation in 4D around the plane [P,Q] where P and Q are
> some vectors, you may select any cutting plane perpendicular to vector R
> from [P,Q] and then rotate the slice around some other vector R1 from [P,Q].
>
> For example, in the most simple situation when bi-axis is
> (1,0,0,0)x(0,1,0,0), one can use it to rotate any of 4 dufferent 3D cells
> (R=(1,0,0,0) or (0,1,0,0)), or any of 4 2D ridges (R=(1,1,0,0) or
> R=(1,-1,0,0)).
>
> When I wrote my description of twist, I thought that if we select vector R1
> perpendicular to R, then it will be an axis of the figure. But now I see
> that it's wrong: if we take R=(1,1,1,1) (0D-centered twist) and perform
> 120-degree rotation, then actual axis R1 will be something like (-3,1,1,1)
> that is not any axis of the tesseract. Of course, I can write in log that
> R1=(0,1,1,1) or (1,0,0,0) (so that [R,R1] gives the rotation bi-axis), but
> such selection will be arbitrary, not canonical, and I'm not sure that the
> rotational bi-axis will always contain two axes of the figure.
>
> It looks like we should enumerate all rotational planes as well as axes,
> and use orthogonal pairs (axis,plane) in the log file.
>
> This method will work for all finite puzzles where twists can be defined in
> 2D way (with D-2 dimensional multy-axis), but there will be a lot of
> external data for the axes set definitions (list of axes, and list of planes
> - and there are some infinite families of sets...) So format will be not as
> elegant as it supposed to be.
>
> For 3^5 there is a restricted set with only 5 axes and 10 rotational planes
> - and only 30 axis/plane pairs may appear in log. For 3^7 there are 7 axes
> and 21 planes (105 possible combinations) an for 5D simplex we have 6 axes
> and 20 planes (or 10? not sure) that give us 120 deg-twists of faces.
>
>
> Andrey
>
> --- In 4D_Cubing@yahoogroups.com, "Andrew Gould" wrote:
> >
> > I'm seeing 46 rotational planes for the tesseract (6 planes for 90-degree
> > rotations, 24 for 180-degree, 16 for 120-degree), now I'm trying to
> > translate into Andrey's 40 axes--I got confused.
> >
> >
> >
> > I'm keeping my so-called "2D twists" in mind. They seem to use the same
> > axes/rotational planes that are already used.
> >
> > http://groups.yahoo.com/group/4D_Cubing/photos/album/1774759718/pic/list
> >
> >
> >
> > The deal in 5D is that you can twist 4D slices, 3D slices, or 2D
> > slices...but again I'm seeing that they all get twisted about
> > axes/rotational planes that are already used for twisting 4D slices.
> >
> >
> >
> > --
> >
> > Andy
>

--0016e6da9343b0f898049d60bd9a
Content-Type: text/html; charset=ISO-8859-1
Content-Transfer-Encoding: quoted-printable

Hi Andy/Andrey,

=A0

I clearly missed the issue Andy raised earlier, so apologies for my pr=
evious=A0email in this thread, which probably appeared as both=A0obvious an=
d a bit of a non sequitur.

=A0

Anyway, I can't help myself from feeling like this is getting quit=
e complicated, which feels a bit unfortunate.=A0 I do like that the new sug=
gestion=A0looks to=A0handle the 5D case now, but I found my mind trying to =
find a way around enumerating the full set of rotational planes in the file=
=A0(especially in the 4D case).=A0 Those will all have to be generated and =
ordered in a specified manner, like the axes.=A0=A0(This left me wondering =
if it would be=A0simpler to specify how to algorithmically=A0generate/order=
stickers.)


=A0

I am uncertain about something else now too (in the 4D case).=A0 Early=
on, Andrey wrote:

=A0

; PADDING-LEFT: 1ex" class=3D"gmail_quote">For every axis we have number an=
d positions of cutting planes.

=A0

The spaces orthogonal to the 4D symmetry axes are 3D.=A0 So it seems a=
cutting plane position will need to contain orientation information as wel=
l (not just a single number of how deep the cut is on the axis).=A0 Is that=
right?=A0 If so, maybe the rotational plane and cutting plane data both re=
ference the same underlying set?


=A0

Best,

Roice


=A0

On Mon, Feb 28, 2011 at 4:32 AM, Andrey r=3D"ltr"><andreyastrelin@ya=
hoo.com
>
wrote:

; PADDING-LEFT: 1ex" class=3D"gmail_quote">Hi Andy,
=A0I see 12 more rot=
ational planes: they have fixed bivectors (1,1,0,0)x(0,0,1,1) with sign cha=
nges and coordinate permutations.

=A0These planes can't be used in 3D-centered twists (because bi-axis do=
esn't contain coordinate vectors), but there is a couple of 180-deg twi=
sts with them:
2D-centered twist is here: <img src=3D""http://groups.yahoo.com/group/4D_Cubing/photos/album/1184359940/pic/527704=
145/view" target=3D"_blank">http://groups.yahoo.com/group/4D_Cubing/photos/=
album/1184359940/pic/527704145/view
" />

and 0D-centered is here: <img src=3D".com/group/4D_Cubing/photos/album/1184359940/pic/579107863/view" target=3D"=
_blank">http://groups.yahoo.com/group/4D_Cubing/photos/album/1184359940/pic=
/579107863/view
" />


So if you have some rotation in 4D around the plane [P,Q] where P and Q=
are some vectors, you may select any cutting plane perpendicular to vector=
R from [P,Q] and then rotate the slice around some other vector R1 from [P=
,Q].


For example, in the most simple situation when bi-axis is (1,0,0,0)x(0,=
1,0,0), one can use it to rotate any of 4 dufferent 3D cells (R=3D(1,0,0,0)=
or (0,1,0,0)), or any of 4 2D ridges (R=3D(1,1,0,0) or R=3D(1,-1,0,0)).>

When I wrote my description of twist, I thought that if we select vector R1=
perpendicular to R, then it will be an axis of the figure. But now I see t=
hat it's wrong: if we take R=3D(1,1,1,1) (0D-centered twist) and perfor=
m 120-degree rotation, then actual axis R1 will be something like (-3,1,1,1=
) that is not any axis of the tesseract. Of course, I can write in log that=
R1=3D(0,1,1,1) or (1,0,0,0) (so that [R,R1] gives the rotation bi-axis), b=
ut such selection will be arbitrary, not canonical, and I'm not sure th=
at the rotational bi-axis will always contain two axes of the figure.


It looks like we should enumerate all rotational planes as well as axes=
, and use orthogonal pairs (axis,plane) in the log file.

This method=
will work for all finite puzzles where twists can be defined in 2D way (wi=
th D-2 dimensional multy-axis), but there will be a lot of external data fo=
r the axes set definitions (list of axes, and list of planes - and there ar=
e some infinite families of sets...) So format will be not as elegant as it=
supposed to be.


For 3^5 there is a restricted set with only 5 axes and 10 rotational pl=
anes - and only 30 axis/plane pairs may appear in log. For 3^7 there are 7 =
axes and 21 planes (105 possible combinations) an for 5D simplex we have 6 =
axes and 20 planes (or 10? not sure) that give us 120 deg-twists of faces.<=
br>


Andrey




--- In 4=
D_Cubing@yahoogroups.com
, "Andrew Gould" <agould@...> w=
rote:
>
> I'm seeing 46 rotational planes for the tesseract=
(6 planes for 90-degree

> rotations, 24 for 180-degree, 16 for 120-degree), now I'm trying t=
o
> translate into Andrey's 40 axes--I got confused.
>
&=
gt;
>
> I'm keeping my so-called "2D twists" in m=
ind. =A0They seem to use the same

> axes/rotational planes that are already used.
>
> =3D"http://groups.yahoo.com/group/4D_Cubing/photos/album/1774759718/pic/lis=
t" target=3D"_blank">http://groups.yahoo.com/group/4D_Cubing/photos/album/1=
774759718/pic/list


>
>
>
> The deal in 5D is that you can twist 4D slices=
, 3D slices, or 2D
> slices...but again I'm seeing that they all =
get twisted about
> axes/rotational planes that are already used for =
twisting 4D slices.

>
>
>
> --
>
> Andy
e>


--0016e6da9343b0f898049d60bd9a--




From: Andrew James Gould <agould@uwm.edu>
Date: Mon, 28 Feb 2011 21:44:32 -0600 (CST)
Subject: Re: [MC4D] Social dream



Hi guys,
No problem, Roice. It opened my mind a bit. I like 4D geometry once I =
get the lingo.=20=20

Speaking of which, what's a cutting plane? In the 2^4 cube, my guess is th=
at there are four: the 3D hyperplanes between slices of cubies, namely, w=
=3D0, x=3D0, y=3D0, and z=3D0. If so, then I agree with Andrey, you may se=
lect any cutting plane perpendicular to any vector R from [P,Q]. You can s=
elect multiple such cutting planes for a single twist to get my 2D slices. =
Technically, one could either take the union or intersection of the subset=
s created by multiple cutting planes. I agree with Roice, this does get co=
mplex.=20=20

Andrey, this afternoon I did a little calculus to verify that your twelve 1=
80-degree rotations do work, but if you cut the tesseract up like MC4D does=
, you can only apply them to the whole tesseract. If you try them on a 4C =
cubie alone, the corners (and 2D faces, etc.) of that cubie run into other =
cubies--same with a 2D slice: cubies run into cubies. Now that I think ab=
out it, your pic does have diagonal cuts. ...(analyzing)...they are correc=
t. Each only uses one cutting plane.=20=20

For your simple bi-axis (1,0,0,0)x(0,1,0,0), you can also rotate four inter=
nal 2D slices on the 3^4 (between R=3D(1,1,0,0) and R=3D(1,-1,0,0), etc.), =
so I count eight 2D slices not including mask layers.=20=20

For your 120-degree twist about R=3D(1,1,1,1): If it were me, I would writ=
e R1=3D(1,0,0,0) in the log--namely, the center of the face that gets rotat=
ed.=20=20

--
Andy



----- Original Message -----
From: "Roice Nelson"
To: "4D Cubing" <4D_Cubing@yahoogroups.com>
Sent: Monday, February 28, 2011 6:18:51 PM
Subject: Re: [MC4D] Social dream







Hi Andy/Andrey,=20

I clearly missed the issue Andy raised earlier, so apologies for my previou=
s email in this thread, which probably appeared as both obvious and a bit o=
f a non sequitur.=20

Anyway, I can't help myself from feeling like this is getting quite complic=
ated, which feels a bit unfortunate. I do like that the new suggestion look=
s to handle the 5D case now, but I found my mind trying to find a way aroun=
d enumerating the full set of rotational planes in the file (especially in =
the 4D case). Those will all have to be generated and ordered in a specifie=
d manner, like the axes. (This left me wondering if it would be simpler to =
specify how to algorithmically generate/order stickers.)=20

I am uncertain about something else now too (in the 4D case). Early on, And=
rey wrote:=20


For every axis we have number and positions of cutting planes.=20

The spaces orthogonal to the 4D symmetry axes are 3D. So it seems a cutting=
plane position will need to contain orientation information as well (not j=
ust a single number of how deep the cut is on the axis). Is that right? If =
so, maybe the rotational plane and cutting plane data both reference the sa=
me underlying set?=20

Best,=20
Roice=20


On Mon, Feb 28, 2011 at 4:32 AM, Andrey < andreyastrelin@yahoo.com > wrote:=
=20


Hi Andy,=20
I see 12 more rotational planes: they have fixed bivectors (1,1,0,0)x(0,0,1=
,1) with sign changes and coordinate permutations.=20
These planes can't be used in 3D-centered twists (because bi-axis doesn't c=
ontain coordinate vectors), but there is a couple of 180-deg twists with th=
em:=20
2D-centered twist is here: bing/photos/album/1184359940/pic/527704145/view " />=20
and 0D-centered is here: ng/photos/album/1184359940/pic/579107863/view " />=20

So if you have some rotation in 4D around the plane [P,Q] where P and Q are=
some vectors, you may select any cutting plane perpendicular to vector R f=
rom [P,Q] and then rotate the slice around some other vector R1 from [P,Q].=
=20

For example, in the most simple situation when bi-axis is (1,0,0,0)x(0,1,0,=
0), one can use it to rotate any of 4 dufferent 3D cells (R=3D(1,0,0,0) or =
(0,1,0,0)), or any of 4 2D ridges (R=3D(1,1,0,0) or R=3D(1,-1,0,0)).=20

When I wrote my description of twist, I thought that if we select vector R1=
perpendicular to R, then it will be an axis of the figure. But now I see t=
hat it's wrong: if we take R=3D(1,1,1,1) (0D-centered twist) and perform 12=
0-degree rotation, then actual axis R1 will be something like (-3,1,1,1) th=
at is not any axis of the tesseract. Of course, I can write in log that R1=
=3D(0,1,1,1) or (1,0,0,0) (so that [R,R1] gives the rotation bi-axis), but =
such selection will be arbitrary, not canonical, and I'm not sure that the =
rotational bi-axis will always contain two axes of the figure.=20

It looks like we should enumerate all rotational planes as well as axes, an=
d use orthogonal pairs (axis,plane) in the log file.=20

This method will work for all finite puzzles where twists can be defined in=
2D way (with D-2 dimensional multy-axis), but there will be a lot of exter=
nal data for the axes set definitions (list of axes, and list of planes - a=
nd there are some infinite families of sets...) So format will be not as el=
egant as it supposed to be.=20

For 3^5 there is a restricted set with only 5 axes and 10 rotational planes=
- and only 30 axis/plane pairs may appear in log. For 3^7 there are 7 axes=
and 21 planes (105 possible combinations) an for 5D simplex we have 6 axes=
and 20 planes (or 10? not sure) that give us 120 deg-twists of faces.=20


Andrey=20




--- In 4D_Cubing@yahoogroups.com , "Andrew Gould" wrote:=20
>=20
> I'm seeing 46 rotational planes for the tesseract (6 planes for 90-degree=
=20
> rotations, 24 for 180-degree, 16 for 120-degree), now I'm trying to=20
> translate into Andrey's 40 axes--I got confused.=20
>=20
>=20
>=20
> I'm keeping my so-called "2D twists" in mind. They seem to use the same=20
> axes/rotational planes that are already used.=20
>=20
> http://groups.yahoo.com/group/4D_Cubing/photos/album/1774759718/pic/list=
=20
>=20
>=20
>=20
> The deal in 5D is that you can twist 4D slices, 3D slices, or 2D=20
> slices...but again I'm seeing that they all get twisted about=20
> axes/rotational planes that are already used for twisting 4D slices.=20
>=20
>=20
>=20
> --=20
>=20
> Andy=20