Thread: "Records: Now with moar images!"

--------------090705060209000602090004
Content-Type: text/plain; charset=ISO-8859-1; format=flowed
Content-Transfer-Encoding: 7bit

Dear Cubists,

I had been thinking that we really needed to sex-up the records and
puzzle pages with images, so I took some screen shots of the {5}x{4} in
several lengths, uploaded them to the wiki, and inserted the appropriate
one into each length section of the {5}x{4} puzzle page
and one example
into the records page .
I think that this turned out quite well and would like to propose that
we do this in general. I would be very grateful if someone would do this
for the rest of the puzzles. This would be a great way for a
non-programmer/non-solver to make a valuable contribution to this
project. I'll be happy to offer suggestions on how to capture, edit,
upload, and format images if anyone has questions.

In related news, notice that the {5}x{4} records now includes the first
length-5 solution by Christopher Locke
.
Well done Christopher!!

-Melinda

--------------090705060209000602090004
Content-Type: text/html; charset=ISO-8859-1
Content-Transfer-Encoding: 7bit






Dear Cubists,



I had been thinking that we really needed to sex-up the records and
puzzle pages with images, so I took some screen shots of the {5}x{4} in
several lengths, uploaded them to the wiki, and inserted the
appropriate one into each length section of the href="http://wiki.superliminal.com/wiki/Pentagonal_Duoprism">{5}x{4}
puzzle page and one example into the href="http://wiki.superliminal.com/wiki/MC4D_Records">records page.
I think that this turned out quite well and would like to propose that
we do this in general. I would be very grateful if someone would do
this for the rest of the puzzles. This would be a great way for a
non-programmer/non-solver to make a valuable contribution to this
project. I'll be happy to offer suggestions on how to capture, edit,
upload, and format images if anyone has questions.



In related news, notice that the {5}x{4} records now includes the first
length-5 solution by href="http://wiki.superliminal.com/wiki/User:Vega12#vega12-5_4_2PentagonalDuoprism.281316.29"
title="User:Vega12">Christopher Locke. Well done Christopher!!



-Melinda




--------------090705060209000602090004--

--0016369fa1bc5454ea04793442ea
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: quoted-printable

Hello everyone!

I would've sent an email off after finishing the length 5 {5}x{4} duoprism,
but it was like 3am my time, so I chose sleep over email. I hope you can
all understand ^^

First, I was asked to give an update on how my solution to the length 2
{6}x{6} duoprism, especially since the program now has the ability to do al=
l
possible twists of these length 2 puzzles, so there are some more
complications that can arise. The main thing I noticed was that you now
need to keep track of the relative orientation of the colors of each torus.
If you put the 2c pieces into place without considering this and you get it
reversed, then you won't be able to solve. I carelessly neglected this, an=
d
ended up chosing the wrong orientation along the way. I was too lazy to
restart and just fixed the problem there. Luckily it wasn't too hard to
just flip the colors of one torus, and then fix the damage. Saved me time,
but not twists :P

Now, the big one is the length 5 duoprism {5}x{4}. I totally didn't expect
to attempt this puzzle, but I was playing around a bit after solving the
{6}x{6} 2, and got toying with the length 5 puzzles, and decided to see if =
I
am able to fix some 1c centers in them. This quickly turned into a a desir=
e
to go for a full solve. When picking which to do, I settled on the {5}x{4}
over the {5}x{5}. While it's true that the {5}x{5} has less move sequences
you need to learn because the two torii are the same shape, the pentagonal
shaped toruses always seem more awkward to work with. Basically, I felt
more comfortable working with the nice cube shaped faces :P. My adversion
to the pentagonal torii seemed to be justified a little though. I had a bi=
t
more trouble finding macros for fixing the centers, faces, and edges of the
pentagonal torus.

By the way, one notational convention I used in my notes and macro names is
the following. We all know and use 1c, 2c, 3c... to describe pieces. In
these duoprisms though, I pointed out previously, there are different kinds
of pieces depending on their locations. For instance, among 2c pieces in
the {5}x{4}, there are 2c pieces between two pentagonal facets, 2c pieces
between a pentagonal and square facet, and 2c pieces between two square
facets (facet is just the term for a hyperface - so in 4D that is a 3D
hyperface which are the 'faces' you twist). I label these different pieces
2c(5,5), 2c(5,4), 2c(4,4). Similarly you can have 1c(5), 1c(4), 3c(5,5,4),
3c(5,4,4).

Because I felt less comfortable with the pentagonal facets, I always made a=
n
effort to fix those blocks first (I also distinguish between 'fixing' piece=
s
as putting the blocks together, and solving them by putting them in the
correct relative location). I was able to fix all the 1c pieces without an=
y
macros thankfully. Then, I worked my way from there, and developed macros
along the way for each of the kinds of blocks present that needed fixing.
One thing that is nice about fixing blocks over placing them, is that you
can freely rotate the blocks into any arbitrary position you want before
applying a macro, and since you aren't yet solving them, you don't need to
be careful about undoing the sequence afterwards (conjugation). This meant
that I was able to use my 3swap algorithms to almost invariably place 2
pieces in the correct block and orientation. When I got to actually solvin=
g
though, sometimes the move sequences to put everything in place to solve 2
pieces is too long to remember how to undo, so I usually settled for less
moves to get one piece in, and as such could cut down that part of the solv=
e
a fair bit.

Oh yeah, I also ran into a problem I had before with the solution to the
reduced {5}x{4} 3 puzzle. In this length 3 puzzle, you can have a case
where you think all your 2c pieces are placed nicely, then end up with a
case where you have to swap just two 2c pieces, which seems at first to be
an impossibility. I found out how to fix this before, and again since I
didn't remember how I fixed it, had to come up with it again, by examining
the effects of each kind of twist. By looking at all the twists, and
determining whether it is an even or odd permutation of 2c pieces, you can
find that by doing a single twist of a square facet, you are doing a 4cycle
of 2c(5,4) pieces, which is odd. So you can basically fix this problem by
using your 3swap algorithm to rotate the 2c(5,4) pieces a quarter-turn, the=
n
you will be left in a case that is more directly solvable. This same
problem can arise in any case where there are odd permutation twists
(therefore, it can also happen in the hexagonal duoprisms).

Anyway, this last step of solving I was able to do actually in less then
half the moves of my first time solving the {5}x{4} 3 due to being more
comfortable with these newer puzzles now. It was quite a marathon of
working a fair bit every night for 3 nights, but it's over now and was wort=
h
it. I'm actually now able to solve my 5^3 cube without having to resort to
any memorized algorithms now because of my experiences with this and other
puzzles. Very cool.

It's late here again, so I'll finish with that. The biggest advice I can
give is that while these bigger puzzles seem intimidating, if you have
patience and some experience with other bigger puzzles (like 4^4 and 5^4)
then even these monsters are conquerable!

Chris

2009/11/25 Melinda Green

>
>
> Dear Cubists,
>
> I had been thinking that we really needed to sex-up the records and puzzl=
e
> pages with images, so I took some screen shots of the {5}x{4} in several
> lengths, uploaded them to the wiki, and inserted the appropriate one into
> each length section of the {5}x{4} puzzle pageom/wiki/Pentagonal_Duoprism>and one example into the records
> page . I think that this
> turned out quite well and would like to propose that we do this in genera=
l.
> I would be very grateful if someone would do this for the rest of the
> puzzles. This would be a great way for a non-programmer/non-solver to mak=
e a
> valuable contribution to this project. I'll be happy to offer suggestions=
on
> how to capture, edit, upload, and format images if anyone has questions.
>
> In related news, notice that the {5}x{4} records now includes the first
> length-5 solution by Christopher LockeUser:Vega12#vega12-5_4_2PentagonalDuoprism.281316.29>.
> Well done Christopher!!
>
> -Melinda
>=20=20
>

--0016369fa1bc5454ea04793442ea
Content-Type: text/html; charset=UTF-8
Content-Transfer-Encoding: quoted-printable

Hello everyone!

I would've sent an email off after finishing the=
length 5 {5}x{4} duoprism, but it was like 3am my time, so I chose sleep o=
ver email.=C2=A0 I hope you can all understand ^^

First, I was asked=
to give an update on how my solution to the length 2 {6}x{6} duoprism, esp=
ecially since the program now has the ability to do all possible twists of =
these length 2 puzzles, so there are some more complications that can arise=
.=C2=A0 The main thing I noticed was that you now need to keep track of the=
relative orientation of the colors of each torus.=C2=A0 If you put the 2c =
pieces into place without considering this and you get it reversed, then yo=
u won't be able to solve.=C2=A0 I carelessly neglected this, and ended =
up chosing the wrong orientation along the way.=C2=A0 I was too lazy to res=
tart and just fixed the problem there.=C2=A0 Luckily it wasn't too hard=
to just flip the colors of one torus, and then fix the damage.=C2=A0 Saved=
me time, but not twists :P


Now, the big one is the length 5 duoprism {5}x{4}.=C2=A0 I totally didn=
't expect to attempt this puzzle, but I was playing around a bit after =
solving the {6}x{6} 2, and got toying with the length 5 puzzles, and decide=
d to see if I am able to fix some 1c centers in them.=C2=A0 This quickly tu=
rned into a a desire to go for a full solve.=C2=A0 When picking which to do=
, I settled on the {5}x{4} over the {5}x{5}.=C2=A0 While it's true that=
the {5}x{5} has less move sequences you need to learn because the two tori=
i are the same shape, the pentagonal shaped toruses always seem more awkwar=
d to work with.=C2=A0 Basically, I felt more comfortable working with the n=
ice cube shaped faces :P.=C2=A0 My adversion to the pentagonal torii seemed=
to be justified a little though.=C2=A0 I had a bit more trouble finding ma=
cros for fixing the centers, faces, and edges of the pentagonal torus.


By the way, one notational convention I used in my notes and macro name=
s is the following.=C2=A0 We all know and use 1c, 2c, 3c... to describe pie=
ces.=C2=A0 In these duoprisms though, I pointed out previously, there are d=
ifferent kinds of pieces depending on their locations.=C2=A0 For instance, =
among 2c pieces in the {5}x{4}, there are 2c pieces between two pentagonal =
facets, 2c pieces between a pentagonal and square facet, and 2c pieces betw=
een two square facets (facet is just the term for a hyperface - so in 4D th=
at is a 3D hyperface which are the 'faces' you twist).=C2=A0 I labe=
l these different pieces 2c(5,5), 2c(5,4), 2c(4,4).=C2=A0 Similarly you can=
have 1c(5), 1c(4), 3c(5,5,4), 3c(5,4,4).


Because I felt less comfortable with the pentagonal facets, I always ma=
de an effort to fix those blocks first (I also distinguish between 'fix=
ing' pieces as putting the blocks together, and solving them by putting=
them in the correct relative location).=C2=A0 I was able to fix all the 1c=
pieces without any macros thankfully.=C2=A0 Then, I worked my way from the=
re, and developed macros along the way for each of the kinds of blocks pres=
ent that needed fixing.=C2=A0 One thing that is nice about fixing blocks ov=
er placing them, is that you can freely rotate the blocks into any arbitrar=
y position you want before applying a macro, and since you aren't yet s=
olving them, you don't need to be careful about undoing the sequence af=
terwards (conjugation).=C2=A0 This meant that I was able to use my 3swap al=
gorithms to almost invariably place 2 pieces in the correct block and orien=
tation.=C2=A0 When I got to actually solving though, sometimes the move seq=
uences to put everything in place to solve 2 pieces is too long to remember=
how to undo, so I usually settled for less moves to get one piece in, and =
as such could cut down that part of the solve a fair bit.


Oh yeah, I also ran into a problem I had before with the solution to th=
e reduced {5}x{4} 3 puzzle.=C2=A0 In this length 3 puzzle, you can have a c=
ase where you think all your 2c pieces are placed nicely, then end up with =
a case where you have to swap just two 2c pieces, which seems at first to b=
e an impossibility.=C2=A0 I found out how to fix this before, and again sin=
ce I didn't remember how I fixed it, had to come up with it again, by e=
xamining the effects of each kind of twist.=C2=A0 By looking at all the twi=
sts, and determining whether it is an even or odd permutation of 2c pieces,=
you can find that by doing a single twist of a square facet, you are doing=
a 4cycle of 2c(5,4) pieces, which is odd.=C2=A0 So you can basically fix t=
his problem by using your 3swap algorithm to rotate the 2c(5,4) pieces a qu=
arter-turn, then you will be left in a case that is more directly solvable.=
=C2=A0 This same problem can arise in any case where there are odd permutat=
ion twists (therefore, it can also happen in the hexagonal duoprisms).


Anyway, this last step of solving I was able to do actually in less the=
n half the moves of my first time solving the {5}x{4} 3 due to being more c=
omfortable with these newer puzzles now.=C2=A0 It was quite a marathon of w=
orking a fair bit every night for 3 nights, but it's over now and was w=
orth it.=C2=A0 I'm actually now able to solve my 5^3 cube without havin=
g to resort to any memorized algorithms now because of my experiences with =
this and other puzzles.=C2=A0 Very cool.


It's late here again, so I'll finish with that.=C2=A0 The bigge=
st advice I can give is that while these bigger puzzles seem intimidating, =
if you have patience and some experience with other bigger puzzles (like 4^=
4 and 5^4) then even these monsters are conquerable!


Chris

--0015175cdafab185740479361e3c
Content-Type: text/plain; charset=ISO-8859-1

Great stuff Chris!

Your block solution approach is interesting.

I also like your notations thoughts. One tiny observation I had was that
there is redundancy in it, so for example 3c(5,5,4) could be reduced to
(5,5,4), or even simply 554 for that matter. In any case, I definitely like
your approach to distinguish between the various kinds of piece types, since
number of colors is not discriminating enough.

There are some other situations that might be relevant to these piece
labeling thoughts. As just one of many examples, there are two types of 4C
pieces on the length-3 simplex (one with 4 tetrahedral stickers and one with
4 octahedral stickers), and again number of colors falls short for
classification. Unfortunately, this time both piece types are connected the
same number and types of faces. I'm not sure how one might be able to
elegantly distinguish those via notation. Maybe sticker shape has to come
into play or something...

Take Care,
Roice


On Wed, Nov 25, 2009 at 10:07 AM, Chris Locke wrote:

>
>
> Hello everyone!
>
> I would've sent an email off after finishing the length 5 {5}x{4} duoprism,
> but it was like 3am my time, so I chose sleep over email. I hope you can
> all understand ^^
>
> First, I was asked to give an update on how my solution to the length 2
> {6}x{6} duoprism, especially since the program now has the ability to do all
> possible twists of these length 2 puzzles, so there are some more
> complications that can arise. The main thing I noticed was that you now
> need to keep track of the relative orientation of the colors of each torus.
> If you put the 2c pieces into place without considering this and you get it
> reversed, then you won't be able to solve. I carelessly neglected this, and
> ended up chosing the wrong orientation along the way. I was too lazy to
> restart and just fixed the problem there. Luckily it wasn't too hard to
> just flip the colors of one torus, and then fix the damage. Saved me time,
> but not twists :P
>
> Now, the big one is the length 5 duoprism {5}x{4}. I totally didn't expect
> to attempt this puzzle, but I was playing around a bit after solving the
> {6}x{6} 2, and got toying with the length 5 puzzles, and decided to see if I
> am able to fix some 1c centers in them. This quickly turned into a a desire
> to go for a full solve. When picking which to do, I settled on the {5}x{4}
> over the {5}x{5}. While it's true that the {5}x{5} has less move sequences
> you need to learn because the two torii are the same shape, the pentagonal
> shaped toruses always seem more awkward to work with. Basically, I felt
> more comfortable working with the nice cube shaped faces :P. My adversion
> to the pentagonal torii seemed to be justified a little though. I had a bit
> more trouble finding macros for fixing the centers, faces, and edges of the
> pentagonal torus.
>
> By the way, one notational convention I used in my notes and macro names is
> the following. We all know and use 1c, 2c, 3c... to describe pieces. In
> these duoprisms though, I pointed out previously, there are different kinds
> of pieces depending on their locations. For instance, among 2c pieces in
> the {5}x{4}, there are 2c pieces between two pentagonal facets, 2c pieces
> between a pentagonal and square facet, and 2c pieces between two square
> facets (facet is just the term for a hyperface - so in 4D that is a 3D
> hyperface which are the 'faces' you twist). I label these different pieces
> 2c(5,5), 2c(5,4), 2c(4,4). Similarly you can have 1c(5), 1c(4), 3c(5,5,4),
> 3c(5,4,4).
>
> Because I felt less comfortable with the pentagonal facets, I always made
> an effort to fix those blocks first (I also distinguish between 'fixing'
> pieces as putting the blocks together, and solving them by putting them in
> the correct relative location). I was able to fix all the 1c pieces without
> any macros thankfully. Then, I worked my way from there, and developed
> macros along the way for each of the kinds of blocks present that needed
> fixing. One thing that is nice about fixing blocks over placing them, is
> that you can freely rotate the blocks into any arbitrary position you want
> before applying a macro, and since you aren't yet solving them, you don't
> need to be careful about undoing the sequence afterwards (conjugation).
> This meant that I was able to use my 3swap algorithms to almost invariably
> place 2 pieces in the correct block and orientation. When I got to actually
> solving though, sometimes the move sequences to put everything in place to
> solve 2 pieces is too long to remember how to undo, so I usually settled for
> less moves to get one piece in, and as such could cut down that part of the
> solve a fair bit.
>
> Oh yeah, I also ran into a problem I had before with the solution to the
> reduced {5}x{4} 3 puzzle. In this length 3 puzzle, you can have a case
> where you think all your 2c pieces are placed nicely, then end up with a
> case where you have to swap just two 2c pieces, which seems at first to be
> an impossibility. I found out how to fix this before, and again since I
> didn't remember how I fixed it, had to come up with it again, by examining
> the effects of each kind of twist. By looking at all the twists, and
> determining whether it is an even or odd permutation of 2c pieces, you can
> find that by doing a single twist of a square facet, you are doing a 4cycle
> of 2c(5,4) pieces, which is odd. So you can basically fix this problem by
> using your 3swap algorithm to rotate the 2c(5,4) pieces a quarter-turn, then
> you will be left in a case that is more directly solvable. This same
> problem can arise in any case where there are odd permutation twists
> (therefore, it can also happen in the hexagonal duoprisms).
>
> Anyway, this last step of solving I was able to do actually in less then
> half the moves of my first time solving the {5}x{4} 3 due to being more
> comfortable with these newer puzzles now. It was quite a marathon of
> working a fair bit every night for 3 nights, but it's over now and was worth
> it. I'm actually now able to solve my 5^3 cube without having to resort to
> any memorized algorithms now because of my experiences with this and other
> puzzles. Very cool.
>
> It's late here again, so I'll finish with that. The biggest advice I can
> give is that while these bigger puzzles seem intimidating, if you have
> patience and some experience with other bigger puzzles (like 4^4 and 5^4)
> then even these monsters are conquerable!
>
> Chris
>
> 2009/11/25 Melinda Green
>
>
>>
>> Dear Cubists,
>>
>> I had been thinking that we really needed to sex-up the records and puzzle
>> pages with images, so I took some screen shots of the {5}x{4} in several
>> lengths, uploaded them to the wiki, and inserted the appropriate one into
>> each length section of the {5}x{4} puzzle pageand one example into the records
>> page . I think that this
>> turned out quite well and would like to propose that we do this in general.
>> I would be very grateful if someone would do this for the rest of the
>> puzzles. This would be a great way for a non-programmer/non-solver to make a
>> valuable contribution to this project. I'll be happy to offer suggestions on
>> how to capture, edit, upload, and format images if anyone has questions.
>>
>> In related news, notice that the {5}x{4} records now includes the first
>> length-5 solution by Christopher Locke.
>> Well done Christopher!!
>>
>> -Melinda
>>
>
>
>
>
>

--0015175cdafab185740479361e3c
Content-Type: text/html; charset=ISO-8859-1
Content-Transfer-Encoding: quoted-printable

Great stuff Chris!