Thread: "Physical 2x2x2x2 - Canonical moves"

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First off, please check out Zander Bolgar's lovely solution video that he invited me to share. It's very cool to see someone developing something like finger tricks and blasting through a solution. It's very much like Bob's and Joel's solutions as well as Marc's approach.

This makes for a great launching point for questions about which moves should be included in a canonical set. Of course any move that results in a reachable state can be justified in a solution, but there's such a spectrum from "obviously fine" to "obviously not". Now that we've gotten some experience with this puzzle and the practicalities of solving it, I feel it's time to see if we can find some sort of natural canonical set, so I'd love to hear your thoughts.

Here is the list of moves I know about, loosely ordered as described above:

1. Simple rotations
2. 90 degree twists of outer face
3. 180 degree twists of side face
4. Center face axial twist
5. Arbitrary half-puzzle juxtapositions
6. Clamshell move
7. Whole-puzzle reorientations
8. 90 degree twist of side face (each 2x2x1 square rotate in opposite directions)
9. Single end cap twist (with parity restrictions?) [fine for scrambling]
10. Restacking moves [fine for scrambling]
11. Single piece flip
12. Reassemble entire puzzle

I suspect the trickiest part has to do with #9 which is the one I would most like to nail down.

I intend to create a follow-up video to talk about all of these and any others you can think of. The way you can help is to offer additions and corrections to the above list, and especially in suggesting ways to reorder it. Then please suggest where you'd draw three lines:

* Everything above is primitive (Or "basic" or "elementary" as Joel calls them)
* Everything above is canonical. IE always acceptable in solutions
* Nothing below is acceptable in solutions.

Thanks all!
-Melinda

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">


First off, please check out href=3D"https://www.youtube.com/watch?v=3DfYxn4wPe2ZE">Zander Bolgar'=
s
lovely solution video that he invited me to share. It's very
cool to see someone developing something like finger tricks and
blasting through a solution. It's very much like moz-do-not-send=3D"true"
href=3D"https://groups.yahoo.com/neo/groups/4D_Cubing/conversations/topics/=
3803">Bob's
and href=3D"https://groups.yahoo.com/neo/groups/4D_Cubing/conversations/message=
s/3904">Joel's
solutions as well as href=3D"https://www.youtube.com/watch?v=3DpKHU5sFaGvY">Marc's
approach.



This makes for a great launching point for questions about which
moves should be included in a canonical set. Of course any move that
results in a reachable state can be justified in a solution, but
there's such a spectrum from "obviously fine" to "obviously not".=C2=A0
Now that we've gotten some experience with this puzzle and the
practicalities of solving it, I feel it's time to see if we can find
some sort of natural canonical set, so I'd love to hear your
thoughts.



Here is the list of moves I know about, loosely ordered as described
above:

1. Simple rotations


2. 90 degree twists of outer face


3. 180 degree twists of side face


4. Center face axial twist


5. Arbitrary half-puzzle juxtapositions


6. Clamshell move


7. Whole-puzzle reorientations


8. 90 degree twist of side face (each 2x2x1 square rotate in
   opposite directions)
   
   


9. Single end cap twist (with parity restrictions?) [fine for
   scrambling]


10. Restacking moves [fine for scrambling]


11. Single piece flip


12. Reassemble entire puzzle
    
    

• Everything above is primitive (Or "basic" or "elementary" as
  Joel calls them)


• Everything above is canonical. IE always acceptable in
  solutions


• Nothing below is acceptable in solutions.

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Oops! Looks like the link has an extra period in it =F0=9F=99=82
https://www.youtube.com/watch?v=3DfYxn4wPe2ZE there's the corrected one for
anyone too lazy

Looking forward to watching the video!

On Thu, Jan 4, 2018, 4:28 PM Melinda Green melinda@superliminal.com
[4D_Cubing] <4D_Cubing@yahoogroups.com> wrote:

>
>
> First off, please check out Zander Bolgar's lovely solution video
> that he invited me to
> share. It's very cool to see someone developing something like finger
> tricks and blasting through a solution. It's very much like Bob's
>
> and Joel's
> 4>
> solutions as well as Marc's Y>
> approach.
>
> This makes for a great launching point for questions about which moves
> should be included in a canonical set. Of course any move that results in=
a
> reachable state can be justified in a solution, but there's such a spectr=
um
> from "obviously fine" to "obviously not". Now that we've gotten some
> experience with this puzzle and the practicalities of solving it, I feel
> it's time to see if we can find some sort of natural canonical set, so I'=
d
> love to hear your thoughts.
>
> Here is the list of moves I know about, loosely ordered as described abov=
e:
>
> 1. Simple rotations
> 2. 90 degree twists of outer face
> 3. 180 degree twists of side face
> 4. Center face axial twist
> 5. Arbitrary half-puzzle juxtapositions
> 6. Clamshell move
> 7. Whole-puzzle reorientations
> 8. 90 degree twist of side face (each 2x2x1 square rotate in opposite
> directions)
> 9. Single end cap twist (with parity restrictions?) [fine for
> scrambling]
> 10. Restacking moves [fine for scrambling]
> 11. Single piece flip
> 12. Reassemble entire puzzle
>
> I suspect the trickiest part has to do with #9 which is the one I would
> most like to nail down.
>
> I intend to create a follow-up video to talk about all of these and any
> others you can think of. The way you can help is to offer additions and
> corrections to the above list, and especially in suggesting ways to reord=
er
> it. Then please suggest where you'd draw three lines:
>
> - Everything above is primitive (Or "basic" or "elementary" as Joel
> calls them)
> - Everything above is canonical. IE always acceptable in solutions
> - Nothing below is acceptable in solutions.
>
> Thanks all!
> -Melinda
>=20
>

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Oops! Looks like the link has an extra period in it =F0=9F=
=99=82 https://ww=
w.youtube.com/watch?v=3DfYxn4wPe2ZE there's the corrected one for a=
nyone too lazy

Looking forward to watching the video!

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Regarding #9: to get solvable states the number of single cap twists has to
be even (a single cap twist is an odd permutation but only even
permutations are possible for the 2^4). I don't think that a single cap
twist breaks the corner rotation restriction so as long as an even number
is used everything should be fine.

Best regards,
Joel


Den 5 jan. 2018 12:33 fm skrev "Ty Jones whotyjones@gmail.com [4D_Cubing]" =
<
4D_Cubing@yahoogroups.com>:



Oops! Looks like the link has an extra period in it =F0=9F=99=82
https://www.youtube.com/watch?v=3DfYxn4wPe2ZE there's the corrected one for
anyone too lazy

Looking forward to watching the video!

On Thu, Jan 4, 2018, 4:28 PM Melinda Green melinda@superliminal.com
[4D_Cubing] <4D_Cubing@yahoogroups.com> wrote:

>
>
> First off, please check out Zander Bolgar's lovely solution video
> that he invited me to
> share. It's very cool to see someone developing something like finger
> tricks and blasting through a solution. It's very much like Bob's
>
> and Joel's
> 4>
> solutions as well as Marc's Y>
> approach.
>
> This makes for a great launching point for questions about which moves
> should be included in a canonical set. Of course any move that results in=
a
> reachable state can be justified in a solution, but there's such a spectr=
um
> from "obviously fine" to "obviously not". Now that we've gotten some
> experience with this puzzle and the practicalities of solving it, I feel
> it's time to see if we can find some sort of natural canonical set, so I'=
d
> love to hear your thoughts.
>
> Here is the list of moves I know about, loosely ordered as described abov=
e:
>
> 1. Simple rotations
> 2. 90 degree twists of outer face
> 3. 180 degree twists of side face
> 4. Center face axial twist
> 5. Arbitrary half-puzzle juxtapositions
> 6. Clamshell move
> 7. Whole-puzzle reorientations
> 8. 90 degree twist of side face (each 2x2x1 square rotate in opposite
> directions)
> 9. Single end cap twist (with parity restrictions?) [fine for
> scrambling]
> 10. Restacking moves [fine for scrambling]
> 11. Single piece flip
> 12. Reassemble entire puzzle
>
> I suspect the trickiest part has to do with #9 which is the one I would
> most like to nail down.
>
> I intend to create a follow-up video to talk about all of these and any
> others you can think of. The way you can help is to offer additions and
> corrections to the above list, and especially in suggesting ways to reord=
er
> it. Then please suggest where you'd draw three lines:
>
> - Everything above is primitive (Or "basic" or "elementary" as Joel
> calls them)
> - Everything above is canonical. IE always acceptable in solutions
> - Nothing below is acceptable in solutions.
>
> Thanks all!
> -Melinda
>
>=20

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Wait, maybe I've answered my own question. If you twist the other half "the=
wrong way", you can easily reduce both to a single end cap twist of 180 de=
grees which should therefore be fine.
-Melinda
PS: About your notation, 'E' works great as an abbreviation for "End".

On 1/4/2018 11:11 PM, Melinda Green melinda@superliminal.com [4D_Cubing] wr=
ote:
>
>
> For people making a set of moves on one half, can you just count your tur=
ns and either make an extra turn on the other half if it's odd? And if so, =
does it matter which direction you make that twist?
> Thanks,
> -Melinda
>
> On 1/4/2018 11:01 PM, Joel Karlsson joelkarlsson97@gmail.com [4D_Cubing] =
wrote:
>> Regarding #9: to get solvable states the number of single cap twists has=
to be even (a single cap twist is an odd permutation but only even permuta=
tions are possible for the 2^4). I don't think that a single cap twist brea=
ks the corner rotation restriction so as long as an even number is used eve=
rything should be fine.
>>
>> Best regards,
>> Joel
>>
>>
>> Den 5 jan. 2018 12:33 fm skrev "Ty Jones whotyjones@gmail.com otyjones@gmail.com> [4D_Cubing]" <4D_Cubing@yahoogroups.com ng@yahoogroups.com>>:
>>
>> Oops! Looks like the link has an extra period in it =F0=9F=99=82 htt=
ps://www.youtube.com/watch?v=3DfYxn4wPe2ZE =3DfYxn4wPe2ZE> there's the corrected one for anyone too lazy
>>
>> Looking forward to watching the video!
>>
>>
>> On Thu, Jan 4, 2018, 4:28 PM Melinda Green melinda@superliminal.com =
[4D_Cubing] <4D_Cubing@yahoogroups.com ailto:4D_Cubing@yahoogroups.com>> wrote:
>>
>> First off, please check out Zander Bolgar's lovely solution vide=
o that he invited me to sh=
are. It's very cool to see someone developing something like finger tricks =
and blasting through a solution. It's very much like Bob's yahoo.com/neo/groups/4D_Cubing/conversations/topics/3803> and Joel's ://groups.yahoo.com/neo/groups/4D_Cubing/conversations/messages/3904> solut=
ions as well as Marc's appr=
oach.
>>
>> This makes for a great launching point for questions about which=
moves should be included in a canonical set. Of course any move that resul=
ts in a reachable state can be justified in a solution, but there's such a =
spectrum from "obviously fine" to "obviously not".=C2=A0 Now that we've got=
ten some experience with this puzzle and the practicalities of solving it, =
I feel it's time to see if we can find some sort of natural canonical set, =
so I'd love to hear your thoughts.
>>
>> Here is the list of moves I know about, loosely ordered as descr=
ibed above:
>>
>> 1. Simple rotations
>> 2. 90 degree twists of outer face
>> 3. 180 degree twists of side face
>> 4. Center face axial twist
>> 5. Arbitrary half-puzzle juxtapositions
>> 6. Clamshell move
>> 7. Whole-puzzle reorientations
>> 8. 90 degree twist of side face (each 2x2x1 square rotate in op=
posite directions)
>> 9. Single end cap twist (with parity restrictions?) [fine for s=
crambling]
>> 10. Restacking moves [fine for scrambling]
>> 11. Single piece flip
>> 12. Reassemble entire puzzle
>>
>> I suspect the trickiest part has to do with #9 which is the one =
I would most like to nail down.
>>
>> I intend to create a follow-up video to talk about all of these =
and any others you can think of. The way you can help is to offer additions=
and corrections to the above list, and especially in suggesting ways to re=
order it. Then please suggest where you'd draw three lines:
>>
>> * Everything above is primitive (Or "basic" or "elementary" as=
Joel calls them)
>> * Everything above is canonical. IE always acceptable in solut=
ions
>> * Nothing below is acceptable in solutions.
>>
>> Thanks all!
>> -Melinda
>>
>>
>
>
>
>=20


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">


Wait, maybe I've answered my own question. If you twist the other
half "the wrong way", you can easily reduce both to a single end cap
twist of 180 degrees which should therefore be fine.

-Melinda

PS: About your notation, 'E' works great as an abbreviation for
"End".

cite=3D"mid:6ca4fe15-6390-259e-525e-b8daf058ad06@superliminal.com">

-8">
For people making a set of
moves on one half, can you just count your turns and either make
an extra turn on the other half if it's odd? And if so, does it
matter which direction you make that twist?

Thanks,

-Melinda

On 1/4/2018 11:01 PM, Joel Karlsson class=3D"moz-txt-link-abbreviated"
href=3D"mailto:joelkarlsson97@gmail.com" moz-do-not-send=3D"true"=
>joelkarlsson97@gmail.com
[4D_Cubing] wrote:

cite=3D"mid:CAEohJcGJPDrtrHA4=3D6S1p8pBiihyf+4sPFP9dr_NTxjXbrLhbw@mail.gmai=
l.com">

Regarding #9: to get solvable states the number of single
cap twists has to be even (a single cap twist is an odd
permutation but only even permutations are possible for the
2^4). I don't think that a single cap twist breaks the
corner rotation restriction so as long as an even number is
used everything should be fine.=C2=A0

Best regards,=C2=A0v>

Joel=C2=A0

Den 5 jan. 2018 12:33 fm skrev
"Ty Jones moz-do-not-send=3D"true">whotyjones@gmail.com
[4D_Cubing]" < href=3D"mailto:4D_Cubing@yahoogroups.com"
moz-do-not-send=3D"true">4D_Cubing@yahoogroups.com>=
;: type=3D"attribution">

.8ex;border-left:1px #ccc solid;padding-left:1ex">

style=3D"display:none">=C2=A0

Oops! Looks like the link has an
extra period in it =F0=9F=99=82 href=3D"https://www.youtube.com/watch?v=3DfYx=
n4wPe2ZE"
target=3D"_blank" moz-do-not-send=3D"true">ht=
tps://www.youtube.com/watch?v=3DfYxn4wPe2ZE
there's the corrected one for anyone too
lazy

Looking forward to watching the
video!

On Thu, Jan 4, 2018, 4:28
PM Melinda Green href=3D"mailto:melinda@superliminal.com"
target=3D"_blank" moz-do-not-send=3D"true=
">melinda@superliminal.com
[4D_Cubing] < href=3D"mailto:4D_Cubing@yahoogroups.com"
target=3D"_blank" moz-do-not-send=3D"true=
">4D_Cubing@yahoogroups.com>
wrote:

style=3D"border-left:1px #ccc solid">

>=C2=A0
id=3D"m_1310257209045721278m_-200042422=
3690736552ygrp-mlmsg">
id=3D"m_1310257209045721278m_-2000424=
223690736552ygrp-msg">
id=3D"m_1310257209045721278m_-20004=
24223690736552ygrp-text">

First off, please check out
href=3D"https://www.youtube..co=
m/watch?v=3DfYxn4wPe2ZE"
target=3D"_blank"
moz-do-not-send=3D"true">Zander
Bolgar's lovely solution
video that he invited me
to share. It's very cool to
see someone developing
something like finger tricks
and blasting through a
solution. It's very much like
href=3D"https://groups.yahoo.com/neo/groups/4D_Cubing/conversations/topics/=
3803"
target=3D"_blank"
moz-do-not-send=3D"true">Bob's<=
/a>
and href=3D"https://groups.yahoo.com/neo/groups/4D_Cubing/conversations/message=
s/3904"
target=3D"_blank"
moz-do-not-send=3D"true">Joel's=

solutions as well as href=3D"https://www.youtube.com=
/watch?v=3DpKHU5sFaGvY"
target=3D"_blank"
moz-do-not-send=3D"true">Marc's=

approach.



This makes for a great
launching point for questions
about which moves should be
included in a canonical set.
Of course any move that
results in a reachable state
can be justified in a
solution, but there's such a
spectrum from "obviously fine"
to "obviously not".=C2=A0 Now tha=
t
we've gotten some experience
with this puzzle and the
practicalities of solving it,
I feel it's time to see if we
can find some sort of natural
canonical set, so I'd love to
hear your thoughts.



Here is the list of moves I
know about, loosely ordered as
described above:

1. Simple rotations


2. 90 degree twists of outer
   face


3. 180 degree twists of side
   face


4. Center face axial twist


5. Arbitrary half-puzzle
   juxtapositions


6. Clamshell move


7. Whole-puzzle
   reorientations


8. 90 degree twist of side
   face (each 2x2x1 square
   rotate in opposite
   directions)
   
   


9. Single end cap twist
   (with parity restrictions?)
   [fine for scrambling]


10. Restacking moves [fine
    for scrambling]


11. Single piece flip


12. Reassemble entire puzzle
    
    

I suspect the trickiest part has
to do with #9 which is the one I
would most like to nail down.



I intend to create a follow-up
video to talk about all of these
and any others you can think of.
The way you can help is to offer
additions and corrections to the
above list, and especially in
suggesting ways to reorder it.
Then please suggest where you'd
draw three lines:

• Everything above is
  primitive (Or "basic" or
  "elementary" as Joel calls
  them)


• Everything above is
  canonical. IE always
  acceptable in solutions


• Nothing below is
  acceptable in solutions.

Thanks all!

-Melinda

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I don't have an opinion on primitive vs. canonical but draw the line
between 8 and 9 for solution acceptability. IOW, I don't consider 9
acceptable for solutions... at least if you want to claim twisting is
faithful to MC4D's 2^4. If you want another fun puzzle, go for it.

9 clearly makes the puzzle easier to solve than in MC4D because it allows
twisting only 4 cubies at a time and dealing with resulting parity at a
later stage. A faithfully modeled twist must permute 8 cubies. I have no
issue with a "twist" being a sequence of moves but it wouldn't be ok would
be to execute move 9, then do some other primitive twists, then execute
move 9 again to fix up parity.

It also feels like a stretch to allow doing something like Melinda
described: manipulating one 2x2x2 block intuitively, then fixing up the
parity on the other block. That is arguably a single twist but manipulates
the puzzle in a fundamentally different way than is possible in MC4D.

I think what I'm suggesting is that allowable twists should traverse the
state space graph in exactly the same way that is possible in MC4D. Hmmmm,
this might eliminate some of the other entries in the list, since I bet a
few of the twists act more like MC4D macros than single twists, so perhaps
this is overly restrictive. Maybe moves like Melinda described should be
allowed. Subtle! However, I do feel pretty strongly that move 9 should be
disallowed in isolation.

Using an even number of 9s during scrambling seems perfectly fine since the
goal of scrambling is just to get a valid puzzle state.

Best,
Roice


On Fri, Jan 5, 2018 at 1:17 AM, Melinda Green melinda@superliminal.com
[4D_Cubing] <4D_Cubing@yahoogroups.com> wrote:

>
>
> Wait, maybe I've answered my own question. If you twist the other half
> "the wrong way", you can easily reduce both to a single end cap twist of
> 180 degrees which should therefore be fine.
> -Melinda
> PS: About your notation, 'E' works great as an abbreviation for "End".
>
>
> On 1/4/2018 11:11 PM, Melinda Green melinda@superliminal.com [4D_Cubing]
> wrote:
>
> For people making a set of moves on one half, can you just count your
> turns and either make an extra turn on the other half if it's odd? And if
> so, does it matter which direction you make that twist?
> Thanks,
> -Melinda
>
> On 1/4/2018 11:01 PM, Joel Karlsson joelkarlsson97@gmail.com [4D_Cubing]
> wrote:
>
> Regarding #9: to get solvable states the number of single cap twists has
> to be even (a single cap twist is an odd permutation but only even
> permutations are possible for the 2^4). I don't think that a single cap
> twist breaks the corner rotation restriction so as long as an even number
> is used everything should be fine.
>
> Best regards,
> Joel
>
>
> Den 5 jan. 2018 12:33 fm skrev "Ty Jones whotyjones@gmail.com
> [4D_Cubing]" <4D_Cubing@yahoogroups.com>:
>
>
>
> Oops! Looks like the link has an extra period in it =F0=9F=99=82
> https://www.youtube.com/watch?v=3DfYxn4wPe2ZE there's the corrected one f=
or
> anyone too lazy
>
> Looking forward to watching the video!
>
> On Thu, Jan 4, 2018, 4:28 PM Melinda Green melinda@superliminal.com
> [4D_Cubing] <4D_Cubing@yahoogroups.com> wrote:
>
>>
>>
>> First off, please check out Zander Bolgar's lovely solution video
>> that he invited me to
>> share. It's very cool to see someone developing something like finger
>> tricks and blasting through a solution. It's very much like Bob's
>> >
>> and Joel's
>> 04>
>> solutions as well as Marc's vY>
>> approach.
>>
>> This makes for a great launching point for questions about which moves
>> should be included in a canonical set. Of course any move that results i=
n a
>> reachable state can be justified in a solution, but there's such a spect=
rum
>> from "obviously fine" to "obviously not". Now that we've gotten some
>> experience with this puzzle and the practicalities of solving it, I feel
>> it's time to see if we can find some sort of natural canonical set, so I=
'd
>> love to hear your thoughts.
>>
>> Here is the list of moves I know about, loosely ordered as described
>> above:
>>
>> 1. Simple rotations
>> 2. 90 degree twists of outer face
>> 3. 180 degree twists of side face
>> 4. Center face axial twist
>> 5. Arbitrary half-puzzle juxtapositions
>> 6. Clamshell move
>> 7. Whole-puzzle reorientations
>> 8. 90 degree twist of side face (each 2x2x1 square rotate in opposite
>> directions)
>> 9. Single end cap twist (with parity restrictions?) [fine for
>> scrambling]
>> 10. Restacking moves [fine for scrambling]
>> 11. Single piece flip
>> 12. Reassemble entire puzzle
>>
>> I suspect the trickiest part has to do with #9 which is the one I would
>> most like to nail down.
>>
>> I intend to create a follow-up video to talk about all of these and any
>> others you can think of. The way you can help is to offer additions and
>> corrections to the above list, and especially in suggesting ways to reor=
der
>> it. Then please suggest where you'd draw three lines:
>>
>> - Everything above is primitive (Or "basic" or "elementary" as Joel
>> calls them)
>> - Everything above is canonical. IE always acceptable in solutions
>> - Nothing below is acceptable in solutions.
>>
>> Thanks all!
>> -Melinda
>>
>
>
>
>
>
>=20
>

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Sure, you violate the permutation parity of the 2^4 hypercube every time
you twist a single 2x2x1 block by 90 degrees (a 4-cycle).  I hope I
didn't say anything to contradict that.

I was, perhaps clumsily, trying to point out that this is "all too easy"
to do by accident during the course of a solve, so one advantage of
allowing the 4-cycle moves is that you're far less likely to find a
frown on your face toward the end of a solve, when you find that you've
strayed into an illegal state.


Marc


On 1/5/2018 11:03 AM, Luna Peña scarecrowfish@gmail.com [4D_Cubing] wrote:
> Wait, I thought you could run into permutation parity by only turning
> the faces of one 2x2x2

As a random half-baked suggestion, I present to you:


The Any8 moveset:   a move is legal if and only if it consists of taking
the puzzle into two equal convex parts (either two 2x2x2 cubes or two
4x2x1 slabs), rearranging them any way you like including twists and
stacks, and placing them together again forming a 4x2x2 block.   Any
such move is legal, and no others.


Since I have previously discovered a full-cube rotation (FUro) that
obeys this constraint, this is a sufficient rule set.  I don't know if
people will like it, but its simplicity has some appeal.


Cheers
Marc

--------------B630214874675E88232580AA
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Content-Transfer-Encoding: quoted-printable

Certainly.

#4 is a twist of the central 2x2x2 block about the long axis. It is a twist=
of the face joining the two halves of the puzzle. It is equivalent to twis=
ting both end caps the opposite direction.

#5 is the first "compound move" that I talk about in the video here //www.youtube.com/watch?v=3D_D4m1Kit3TI&t=3D1m39s> as a natural consequence=
of combining simple rotations with 90 degree twists.

#7 is the fancy 4D change of projection described in the first link in the =
description here .

-Melinda

On 1/5/2018 9:54 AM, Luna Pe=C3=B1a scarecrowfish@gmail.com [4D_Cubing] wro=
te:
>
>
> Can I get clearer definitions of 4, 5 and 7?
>
> ~Luna
>
> On 4 Jan 2018 23:28, "Melinda Green melinda@superliminal.com nda@superliminal.com> [4D_Cubing]" <4D_Cubing@yahoogroups.com bing@yahoogroups.com>> wrote:
>
> First off, please check out Zander Bolgar's lovely solution video tps://www.youtube..com/watch?v=3DfYxn4wPe2ZE> that he invited me to share. =
It's very cool to see someone developing something like finger tricks and b=
lasting through a solution. It's very much like Bob's .com/neo/groups/4D_Cubing/conversations/topics/3803> and Joel's oups.yahoo.com/neo/groups/4D_Cubing/conversations/messages/3904> solutions =
as well as Marc's approach.
>
> This makes for a great launching point for questions about which move=
s should be included in a canonical set. Of course any move that results in=
a reachable state can be justified in a solution, but there's such a spect=
rum from "obviously fine" to "obviously not".=C2=A0 Now that we've gotten s=
ome experience with this puzzle and the practicalities of solving it, I fee=
l it's time to see if we can find some sort of natural canonical set, so I'=
d love to hear your thoughts.
>
> Here is the list of moves I know about, loosely ordered as described =
above:
>
> 1. Simple rotations
> 2. 90 degree twists of outer face
> 3. 180 degree twists of side face
> 4. Center face axial twist
> 5. Arbitrary half-puzzle juxtapositions
> 6. Clamshell move
> 7. Whole-puzzle reorientations
> 8. 90 degree twist of side face (each 2x2x1 square rotate in opposit=
e directions)
> 9. Single end cap twist (with parity restrictions?) [fine for scramb=
ling]
> 10. Restacking moves [fine for scrambling]
> 11. Single piece flip
> 12. Reassemble entire puzzle
>
> I suspect the trickiest part has to do with #9 which is the one I wou=
ld most like to nail down.
>
> I intend to create a follow-up video to talk about all of these and a=
ny others you can think of. The way you can help is to offer additions and =
corrections to the above list, and especially in suggesting ways to reorder=
it. Then please suggest where you'd draw three lines:
>
> * Everything above is primitive (Or "basic" or "elementary" as Joel=
calls them)
> * Everything above is canonical. IE always acceptable in solutions
> * Nothing below is acceptable in solutions.
>
> Thanks all!
> -Melinda
>
>
>
>=20


--------------B630214874675E88232580AA
Content-Type: text/html; charset=utf-8
Content-Transfer-Encoding: quoted-printable



">


Certainly.



#4 is a twist of the central 2x2x2 block about the long axis. It is
a twist of the face joining the two halves of the puzzle. It is
equivalent to twisting both end caps the opposite direction.



#5 is the first "compound move" that I talk about in the video moz-do-not-send=3D"true"
href=3D"https://www.youtube.com/watch?v=3D_D4m1Kit3TI&t=3D1m39s">=
here
as a natural consequence of combining simple rotations with 90
degree twists.



#7 is the fancy 4D change of projection described in the first link
in the description href=3D"https://www.youtube.com/watch?v=3Dd2Fh_1m0UVY">here.



-Melinda

cite=3D"mid:CAK-NJMD8i=3DP7Bpg=3Dhtykwvmt_y4EBbcEZ3bG9JdjtfNyfy+RYQ@mail.gm=
ail.com">

Can I get clearer definitions of 4, 5 and 7?

~Luna

On 4 Jan 2018 23:28, "Melinda Green href=3D"mailto:melinda@superliminal.com"
moz-do-not-send=3D"true">melinda@superliminal.com
[4D_Cubing]" < moz-do-not-send=3D"true">4D_Cubing@yahoogroups.com>
wrote:

.8ex;border-left:1px #ccc solid;padding-left:1ex">

=C2=A0

First off, please check out href=3D"https://www.youtube..com/watch?v=3DfYxn4wPe=
2ZE"
target=3D"_blank" moz-do-not-send=3D"true">Zander
Bolgar's lovely solution video that he
invited me to share. It's very cool to see someone
developing something like finger tricks and
blasting through a solution. It's very much like href=3D"https://groups.yahoo.com/neo/groups/4D_Cubing/conversations/topics/=
3803"
target=3D"_blank" moz-do-not-send=3D"true">Bob's>
and href=3D"https://groups.yahoo.com/neo/groups/4D_Cubing/conversations/message=
s/3904"
target=3D"_blank" moz-do-not-send=3D"true">Joel'sa>
solutions as well as href=3D"https://www.youtube.com/watch?v=3DpKHU5sFaG=
vY"
target=3D"_blank" moz-do-not-send=3D"true">Marc'sa>
approach.



This makes for a great launching point for
questions about which moves should be included in
a canonical set. Of course any move that results
in a reachable state can be justified in a
solution, but there's such a spectrum from
"obviously fine" to "obviously not".=C2=A0 Now that
we've gotten some experience with this puzzle and
the practicalities of solving it, I feel it's time
to see if we can find some sort of natural
canonical set, so I'd love to hear your thoughts.



Here is the list of moves I know about, loosely
ordered as described above:

1. Simple rotations


2. 90 degree twists of outer face


3. 180 degree twists of side face


4. Center face axial twist


5. Arbitrary half-puzzle juxtapositions


6. Clamshell move


7. Whole-puzzle reorientations


8. 90 degree twist of side face (each 2x2x1
   square rotate in opposite directions)
   
   


9. Single end cap twist (with parity
   restrictions?) [fine for scrambling]


10. Restacking moves [fine for scrambling]


11. Single piece flip


12. Reassemble entire puzzle
    
    

I suspect the trickiest part has to do with #9 which
is the one I would most like to nail down.



I intend to create a follow-up video to talk about
all of these and any others you can think of. The
way you can help is to offer additions and
corrections to the above list, and especially in
suggesting ways to reorder it. Then please suggest
where you'd draw three lines:

• Everything above is primitive (Or "basic" or
  "elementary" as Joel calls them)


• Everything above is canonical. IE always
  acceptable in solutions


• Nothing below is acceptable in solutions.

Thanks all!

-Melinda

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

--001a1141ca189c1e6d056212085d
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

OK. Given that, I'd say that:

1-5 are primitive.

7-8 are canonical.

(The rest of ROIL (as in, other twists of the centre 2x2x2 and the
restacked IO twists) may be canonical or may require labeling. I am
unsure.)

6&9(&10?) only with clear labeling (ie. counted as a separate kind of
solve, like macro vs non-macro in MC4D). 11 could possibly be included at a
stretch.

12 is unacceptable.

~Luna

On 6 Jan 2018 01:45, "Melinda Green melinda@superliminal.com [4D_Cubing]" <
4D_Cubing@yahoogroups.com> wrote:



Certainly.

#4 is a twist of the central 2x2x2 block about the long axis. It is a twist
of the face joining the two halves of the puzzle. It is equivalent to
twisting both end caps the opposite direction.

#5 is the first "compound move" that I talk about in the video here
as a natural
consequence of combining simple rotations with 90 degree twists.

#7 is the fancy 4D change of projection described in the first link in the
description here .

-Melinda


On 1/5/2018 9:54 AM, Luna Pe=C3=B1a scarecrowfish@gmail.com [4D_Cubing] wro=
te:

Can I get clearer definitions of 4, 5 and 7?

~Luna

On 4 Jan 2018 23:28, "Melinda Green melinda@superliminal.com [4D_Cubing]" <
4D_Cubing@yahoogroups.com> wrote:

>
>
> First off, please check out Zander Bolgar's lovely solution video
> that he invited me to
> share. It's very cool to see someone developing something like finger
> tricks and blasting through a solution. It's very much like Bob's
>
> and Joel's
> 4>
> solutions as well as Marc's Y>
> approach.
>
> This makes for a great launching point for questions about which moves
> should be included in a canonical set. Of course any move that results in=
a
> reachable state can be justified in a solution, but there's such a spectr=
um
> from "obviously fine" to "obviously not". Now that we've gotten some
> experience with this puzzle and the practicalities of solving it, I feel
> it's time to see if we can find some sort of natural canonical set, so I'=
d
> love to hear your thoughts.
>
> Here is the list of moves I know about, loosely ordered as described abov=
e:
>
> 1. Simple rotations
> 2. 90 degree twists of outer face
> 3. 180 degree twists of side face
> 4. Center face axial twist
> 5. Arbitrary half-puzzle juxtapositions
> 6. Clamshell move
> 7. Whole-puzzle reorientations
> 8. 90 degree twist of side face (each 2x2x1 square rotate in opposite
> directions)
> 9. Single end cap twist (with parity restrictions?) [fine for
> scrambling]
> 10. Restacking moves [fine for scrambling]
> 11. Single piece flip
> 12. Reassemble entire puzzle
>
> I suspect the trickiest part has to do with #9 which is the one I would
> most like to nail down.
>
> I intend to create a follow-up video to talk about all of these and any
> others you can think of. The way you can help is to offer additions and
> corrections to the above list, and especially in suggesting ways to reord=
er
> it. Then please suggest where you'd draw three lines:
>
> - Everything above is primitive (Or "basic" or "elementary" as Joel
> calls them)
> - Everything above is canonical. IE always acceptable in solutions
> - Nothing below is acceptable in solutions.
>
> Thanks all!
> -Melinda
>



--001a1141ca189c1e6d056212085d
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

--------------863D42C5A0F1114A1377A0DE
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Transfer-Encoding: quoted-printable

That's very helpful, Luna, but I'm curious: Why do you see #5 as primitive =
but not #6? Seems to me like it should be both or neither.
-Melinda

On 1/5/2018 6:07 PM, Luna Pe=C3=B1a scarecrowfish@gmail.com [4D_Cubing] wro=
te:
>
>
> OK. Given that, I'd say that:
>
> 1-5 are primitive.
>
> 7-8 are canonical.
>
> (The rest of ROIL (as in, other twists of the centre 2x2x2 and the restac=
ked IO twists) may be canonical or may require labeling. I am unsure.)
>
> 6&9(&10?) only with clear labeling (ie. counted as a separate kind of sol=
ve, like macro vs non-macro in MC4D). 11 could possibly be included at a st=
retch.
>
> 12 is unacceptable.
>
> ~Luna
>
> On 6 Jan 2018 01:45, "Melinda Green melinda@superliminal.com nda@superliminal.com> [4D_Cubing]" <4D_Cubing@yahoogroups.com bing@yahoogroups.com>> wrote:
>
> Certainly.
>
> #4 is a twist of the central 2x2x2 block about the long axis. It is a=
twist of the face joining the two halves of the puzzle. It is equivalent t=
o twisting both end caps the opposite direction.
>
> #5 is the first "compound move" that I talk about in the video here <=
https://www.youtube.com/watch?v=3D_D4m1Kit3TI&t=3D1m39s> as a natural conse=
quence of combining simple rotations with 90 degree twists.
>
> #7 is the fancy 4D change of projection described in the first link i=
n the description here .
>
> -Melinda
>
>
>
> On 1/5/2018 9:54 AM, Luna Pe=C3=B1a scarecrowfish@gmail.com carecrowfish@gmail.com> [4D_Cubing] wrote:
>> Can I get clearer definitions of 4, 5 and 7?
>>
>> ~Luna
>>
>> On 4 Jan 2018 23:28, "Melinda Green melinda@superliminal.com :melinda@superliminal.com> [4D_Cubing]" <4D_Cubing@yahoogroups.com 4D_Cubing@yahoogroups.com>> wrote:
>>
>> First off, please check out Zander Bolgar's lovely solution vide=
o that he invited me to sh=
are. It's very cool to see someone developing something like finger tricks =
and blasting through a solution. It's very much like Bob's yahoo.com/neo/groups/4D_Cubing/conversations/topics/3803> and Joel's ://groups.yahoo.com/neo/groups/4D_Cubing/conversations/messages/3904> solut=
ions as well as Marc's appr=
oach.
>>
>> This makes for a great launching point for questions about which=
moves should be included in a canonical set. Of course any move that resul=
ts in a reachable state can be justified in a solution, but there's such a =
spectrum from "obviously fine" to "obviously not".=C2=A0 Now that we've got=
ten some experience with this puzzle and the practicalities of solving it, =
I feel it's time to see if we can find some sort of natural canonical set, =
so I'd love to hear your thoughts.
>>
>> Here is the list of moves I know about, loosely ordered as descr=
ibed above:
>>
>> 1. Simple rotations
>> 2. 90 degree twists of outer face
>> 3. 180 degree twists of side face
>> 4. Center face axial twist
>> 5. Arbitrary half-puzzle juxtapositions
>> 6. Clamshell move
>> 7. Whole-puzzle reorientations
>> 8. 90 degree twist of side face (each 2x2x1 square rotate in op=
posite directions)
>> 9. Single end cap twist (with parity restrictions?) [fine for s=
crambling]
>> 10. Restacking moves [fine for scrambling]
>> 11. Single piece flip
>> 12. Reassemble entire puzzle
>>
>> I suspect the trickiest part has to do with #9 which is the one =
I would most like to nail down.
>>
>> I intend to create a follow-up video to talk about all of these =
and any others you can think of. The way you can help is to offer additions=
and corrections to the above list, and especially in suggesting ways to re=
order it. Then please suggest where you'd draw three lines:
>>
>> * Everything above is primitive (Or "basic" or "elementary" as=
Joel calls them)
>> * Everything above is canonical. IE always acceptable in solut=
ions
>> * Nothing below is acceptable in solutions.
>>
>> Thanks all!
>> -Melinda
>>
>
>
>
>
>=20


--------------863D42C5A0F1114A1377A0DE
Content-Type: text/html; charset=utf-8
Content-Transfer-Encoding: quoted-printable



">


That's very helpful, Luna, but I'm curious: Why do you see #5 as
primitive but not #6? Seems to me like it should be both or neither.>
-Melinda

cite=3D"mid:CAK-NJMD-Uvdne1PEOSr-g1PKx-SLdRY=3DeTMv8vy0fyTHemJzrA@mail.gmai=
l.com">

OK. Given that, I'd say that:

1-5 are primitive.

7-8 are canonical.=C2=A0

(The rest of ROIL (as in, other twists of the
centre 2x2x2 and the restacked IO twists) may be canonical or
may require labeling. I am unsure.) =C2=A0

6&9(&10?) only with clear labeling (ie.
counted as a separate kind of solve, like macro vs non-macro
in MC4D). 11 could possibly be included at a stretch.

12 is unacceptable.=C2=A0

~Luna

On 6 Jan 2018 01:45, "Melinda Green
moz-do-not-send=3D"true">melinda@superliminal.com
[4D_Cubing]" < href=3D"mailto:4D_Cubing@yahoogroups.com"
moz-do-not-send=3D"true">4D_Cubing@yahoogroups.com>
wrote:

.8ex;border-left:1px #ccc solid;padding-left:1ex">

=C2=A0

Certainly.



#4 is a twist of the central 2x2x2 block about
the long axis. It is a twist of the face
joining the two halves of the puzzle. It is
equivalent to twisting both end caps the
opposite direction.



#5 is the first "compound move" that I talk
about in the video href=3D"https://www.youtube.com/watch?v=3D_D4m1=
Kit3TI&t=3D1m39s"
target=3D"_blank" moz-do-not-send=3D"true">here=

as a natural consequence of combining simple
rotations with 90 degree twists.



#7 is the fancy 4D change of projection
described in the first link in the description
href=3D"https://www.youtube.com/watch?v=3Dd2Fh_=
1m0UVY"
target=3D"_blank" moz-do-not-send=3D"true">here=
.



-Melinda

class=3D"m_1161542213992904350moz-cite-prefix">=
On
1/5/2018 9:54 AM, Luna Pe=C3=B1a class=3D"m_1161542213992904350moz-txt-link-ab=
breviated"
href=3D"mailto:scarecrowfish@gmail.com"
target=3D"_blank" moz-do-not-send=3D"true">sc=
arecrowfish@gmail.com
[4D_Cubing] wrote:

Can I get clearer
definitions of 4, 5 and 7?

~Luna

On 4 Jan 2018
23:28, "Melinda Green href=3D"mailto:melinda@superliminal.com"
target=3D"_blank" moz-do-not-send=3D"true=
">melinda@superliminal.com
[4D_Cubing]" < href=3D"mailto:4D_Cubing@yahoogroups.com"
target=3D"_blank" moz-do-not-send=3D"true=
">4D_Cubing@yahoogroups.com>
wrote:

style=3D"border-left:1px #ccc solid">

an>=C2=A0
id=3D"m_1161542213992904350m_-6533444=
127507305308ygrp-mlmsg">
id=3D"m_1161542213992904350m_-65334=
44127507305308ygrp-msg">
id=3D"m_1161542213992904350m_-653=
3444127507305308ygrp-text">

First off, please check
out href=3D"https://www.youtube..=
com/watch?v=3DfYxn4wPe2ZE"
target=3D"_blank"
moz-do-not-send=3D"true">Zand=
er
Bolgar's lovely solution
video that he invited
me to share. It's very cool
to see someone developing
something like finger tricks
and blasting through a
solution. It's very much
like href=3D"https://groups.yahoo.com/neo/groups/4D_Cubing/conversations/topics/=
3803"
target=3D"_blank"
moz-do-not-send=3D"true">Bob'=
s
and href=3D"https://groups.yahoo.com/neo/groups/4D_Cubing/conversations/message=
s/3904"
target=3D"_blank"
moz-do-not-send=3D"true">Joel=
's
solutions as well as href=3D"https://www.youtube.c=
om/watch?v=3DpKHU5sFaGvY"
target=3D"_blank"
moz-do-not-send=3D"true">Marc=
's
approach.



This makes for a great
launching point for
questions about which moves
should be included in a
canonical set. Of course any
move that results in a
reachable state can be
justified in a solution, but
there's such a spectrum from
"obviously fine" to
"obviously not".=C2=A0 Now that
we've gotten some experience
with this puzzle and the
practicalities of solving
it, I feel it's time to see
if we can find some sort of
natural canonical set, so
I'd love to hear your
thoughts.



Here is the list of moves I
know about, loosely ordered
as described above:

1. Simple rotations


2. 90 degree twists of
   outer face


3. 180 degree twists of
   side face


4. Center face axial twisti>
   
5. Arbitrary half-puzzle
   juxtapositions


6. Clamshell move


7. Whole-puzzle
   reorientations


8. 90 degree twist of side
   face (each 2x2x1 square
   rotate in opposite
   directions)
   
   


9. Single end cap twist
   (with parity
   restrictions?) [fine for
   scrambling]


10. Restacking moves [fine
    for scrambling]


11. Single piece flip


12. Reassemble entire puzzle>
    

I suspect the trickiest part
has to do with #9 which is the
one I would most like to nail
down.



I intend to create a follow-up
video to talk about all of
these and any others you can
think of. The way you can help
is to offer additions and
corrections to the above list,
and especially in suggesting
ways to reorder it. Then
please suggest where you'd
draw three lines:

• Everything above is
  primitive (Or "basic" or
  "elementary" as Joel calls
  them)


• Everything above is
  canonical. IE always
  acceptable in solutions


• Nothing below is
  acceptable in solutions.

Thanks all!

-Melinda

--089e08e4ce3342ec6a0562126a35
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

I see 5 as the equivalent of doing R L on a 2^3, which is obviously just
two twists. However, it is not as obvious to me how 6 is simple twists.
Perhaps when I get my puzzle and see exactly what it does to the puzzle,
I'll change my mind, but I would only class moves that are simple on both
the physical and virtual puzzle as primitive.

~Luna

On 6 Jan 2018 02:32, "Melinda Green melinda@superliminal.com [4D_Cubing]" <
4D_Cubing@yahoogroups.com> wrote:



That's very helpful, Luna, but I'm curious: Why do you see #5 as primitive
but not #6? Seems to me like it should be both or neither.
-Melinda


On 1/5/2018 6:07 PM, Luna Pe=C3=B1a scarecrowfish@gmail.com [4D_Cubing] wro=
te:

OK. Given that, I'd say that:

1-5 are primitive.

7-8 are canonical.

(The rest of ROIL (as in, other twists of the centre 2x2x2 and the
restacked IO twists) may be canonical or may require labeling. I am
unsure.)

6&9(&10?) only with clear labeling (ie. counted as a separate kind of
solve, like macro vs non-macro in MC4D). 11 could possibly be included at a
stretch.

12 is unacceptable.

~Luna

On 6 Jan 2018 01:45, "Melinda Green melinda@superliminal.com [4D_Cubing]" <
4D_Cubing@yahoogroups.com> wrote:



Certainly.

#4 is a twist of the central 2x2x2 block about the long axis. It is a twist
of the face joining the two halves of the puzzle. It is equivalent to
twisting both end caps the opposite direction.

#5 is the first "compound move" that I talk about in the video here
as a natural
consequence of combining simple rotations with 90 degree twists.

#7 is the fancy 4D change of projection described in the first link in the
description here .

-Melinda


On 1/5/2018 9:54 AM, Luna Pe=C3=B1a scarecrowfish@gmail.com [4D_Cubing] wro=
te:

Can I get clearer definitions of 4, 5 and 7?

~Luna

On 4 Jan 2018 23:28, "Melinda Green melinda@superliminal.com [4D_Cubing]" <
4D_Cubing@yahoogroups.com> wrote:

>
>
> First off, please check out Zander Bolgar's lovely solution video
> that he invited me to
> share. It's very cool to see someone developing something like finger
> tricks and blasting through a solution. It's very much like Bob's
>
> and Joel's
> 4>
> solutions as well as Marc's Y>
> approach.
>
> This makes for a great launching point for questions about which moves
> should be included in a canonical set. Of course any move that results in=
a
> reachable state can be justified in a solution, but there's such a spectr=
um
> from "obviously fine" to "obviously not". Now that we've gotten some
> experience with this puzzle and the practicalities of solving it, I feel
> it's time to see if we can find some sort of natural canonical set, so I'=
d
> love to hear your thoughts.
>
> Here is the list of moves I know about, loosely ordered as described abov=
e:
>
> 1. Simple rotations
> 2. 90 degree twists of outer face
> 3. 180 degree twists of side face
> 4. Center face axial twist
> 5. Arbitrary half-puzzle juxtapositions
> 6. Clamshell move
> 7. Whole-puzzle reorientations
> 8. 90 degree twist of side face (each 2x2x1 square rotate in opposite
> directions)
> 9. Single end cap twist (with parity restrictions?) [fine for
> scrambling]
> 10. Restacking moves [fine for scrambling]
> 11. Single piece flip
> 12. Reassemble entire puzzle
>
> I suspect the trickiest part has to do with #9 which is the one I would
> most like to nail down.
>
> I intend to create a follow-up video to talk about all of these and any
> others you can think of. The way you can help is to offer additions and
> corrections to the above list, and especially in suggesting ways to reord=
er
> it. Then please suggest where you'd draw three lines:
>
> - Everything above is primitive (Or "basic" or "elementary" as Joel
> calls them)
> - Everything above is canonical. IE always acceptable in solutions
> - Nothing below is acceptable in solutions.
>
> Thanks all!
> -Melinda
>





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#6 is equivalent to three simple 180 degree twists like I demonstrated here=
.
-Melinda

On 1/5/2018 6:35 PM, Luna Pe=C3=B1a scarecrowfish@gmail.com [4D_Cubing] wro=
te:
>
>
> I see 5 as the equivalent of doing R L on a 2^3, which is obviously just =
two twists. However, it is not as obvious to me how 6 is simple twists. Per=
haps when I get my puzzle and see exactly what it does to the puzzle, I'll =
change my mind, but I would only class moves that are simple on both the ph=
ysical and virtual puzzle as primitive.
>
> ~Luna
>
> On 6 Jan 2018 02:32, "Melinda Green melinda@superliminal.com nda@superliminal.com> [4D_Cubing]" <4D_Cubing@yahoogroups.com bing@yahoogroups.com>> wrote:
>
> That's very helpful, Luna, but I'm curious: Why do you see #5 as prim=
itive but not #6? Seems to me like it should be both or neither.
> -Melinda
>
>
>
> On 1/5/2018 6:07 PM, Luna Pe=C3=B1a scarecrowfish@gmail.com carecrowfish@gmail.com> [4D_Cubing] wrote:
>> OK. Given that, I'd say that:
>>
>> 1-5 are primitive.
>>
>> 7-8 are canonical.
>>
>> (The rest of ROIL (as in, other twists of the centre 2x2x2 and the r=
estacked IO twists) may be canonical or may require labeling. I am unsure.)
>>
>> 6&9(&10?) only with clear labeling (ie. counted as a separate kind o=
f solve, like macro vs non-macro in MC4D). 11 could possibly be included at=
a stretch.
>>
>> 12 is unacceptable.
>>
>> ~Luna
>>
>> On 6 Jan 2018 01:45, "Melinda Green melinda@superliminal.com :melinda@superliminal.com> [4D_Cubing]" <4D_Cubing@yahoogroups.com 4D_Cubing@yahoogroups..com>> wrote:
>>
>> Certainly.
>>
>> #4 is a twist of the central 2x2x2 block about the long axis. It=
is a twist of the face joining the two halves of the puzzle. It is equival=
ent to twisting both end caps the opposite direction.
>>
>> #5 is the first "compound move" that I talk about in the video h=
ere as a natura=
l consequence of combining simple rotations with 90 degree twists.
>>
>> #7 is the fancy 4D change of projection described in the first l=
ink in the description here =
.
>>
>> -Melinda
>>
>>
>>
>> On 1/5/2018 9:54 AM, Luna Pe=C3=B1a scarecrowfish@gmail.com lto:scarecrowfish@gmail.com> [4D_Cubing] wrote:
>>> Can I get clearer definitions of 4, 5 and 7?
>>>
>>> ~Luna
>>>
>>> On 4 Jan 2018 23:28, "Melinda Green melinda@superliminal.com ailto:melinda@superliminal.com> [4D_Cubing]" <4D_Cubing@yahoogroups.com ilto:4D_Cubing@yahoogroups.com>> wrote:
>>>
>>> First off, please check out Zander Bolgar's lovely solution=
video that he invited me =
to share. It's very cool to see someone developing something like finger tr=
icks and blasting through a solution. It's very much like Bob's oups.yahoo.com/neo/groups/4D_Cubing/conversations/topics/3803> and Joel's <=
https://groups.yahoo.com/neo/groups/4D_Cubing/conversations/messages/3904> =
solutions as well as Marc's =
approach.
>>>
>>> This makes for a great launching point for questions about =
which moves should be included in a canonical set. Of course any move that =
results in a reachable state can be justified in a solution, but there's su=
ch a spectrum from "obviously fine" to "obviously not".=C2=A0 Now that we'v=
e gotten some experience with this puzzle and the practicalities of solving=
it, I feel it's time to see if we can find some sort of natural canonical =
set, so I'd love to hear your thoughts.
>>>
>>> Here is the list of moves I know about, loosely ordered as =
described above:
>>>
>>> 1. Simple rotations
>>> 2. 90 degree twists of outer face
>>> 3. 180 degree twists of side face
>>> 4. Center face axial twist
>>> 5. Arbitrary half-puzzle juxtapositions
>>> 6. Clamshell move
>>> 7. Whole-puzzle reorientations
>>> 8. 90 degree twist of side face (each 2x2x1 square rotate =
in opposite directions)
>>> 9. Single end cap twist (with parity restrictions?) [fine =
for scrambling]
>>> 10. Restacking moves [fine for scrambling]
>>> 11. Single piece flip
>>> 12. Reassemble entire puzzle
>>>
>>> I suspect the trickiest part has to do with #9 which is the=
one I would most like to nail down.
>>>
>>> I intend to create a follow-up video to talk about all of t=
hese and any others you can think of. The way you can help is to offer addi=
tions and corrections to the above list, and especially in suggesting ways =
to reorder it. Then please suggest where you'd draw three lines:
>>>
>>> * Everything above is primitive (Or "basic" or "elementar=
y" as Joel calls them)
>>> * Everything above is canonical. IE always acceptable in =
solutions
>>> * Nothing below is acceptable in solutions.
>>>
>>> Thanks all!
>>> -Melinda
>>>
>>
>>
>
>
>
>
>=20


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">


#6 is equivalent to three simple 180 degree twists like I
demonstrated href=3D"https://www.youtube.com/watch?v=3D_D4m1Kit3TI&t=3D1m58s">=
here.

-Melinda

cite=3D"mid:CAK-NJMBRFkk-05i2upOZ=3DQhOmO+nr0Ng-QAovCXvrfngMyA-wQ@mail.gmai=
l.com">

I see 5 as the equivalent of doing R L on a 2^3, which is
obviously just two twists. However, it is not as obvious to me
how 6 is simple twists. Perhaps when I get my puzzle and see
exactly what it does to the puzzle, I'll change my mind, but I
would only class moves that are simple on both the physical
and virtual puzzle as primitive.

~Luna=C2=A0

On 6 Jan 2018 02:32, "Melinda Green
moz-do-not-send=3D"true">melinda@superliminal.com
[4D_Cubing]" < href=3D"mailto:4D_Cubing@yahoogroups.com"
moz-do-not-send=3D"true">4D_Cubing@yahoogroups.com>
wrote:

.8ex;border-left:1px #ccc solid;padding-left:1ex">

=C2=A0

That's very helpful, Luna, but I'm curious:
Why do you see #5 as primitive but not #6?
Seems to me like it should be both or neither.>
-Melinda

class=3D"m_8311926157861543071moz-cite-prefix">=
On
1/5/2018 6:07 PM, Luna Pe=C3=B1a class=3D"m_8311926157861543071moz-txt-link-ab=
breviated"
href=3D"mailto:scarecrowfish@gmail.com"
target=3D"_blank" moz-do-not-send=3D"true">sc=
arecrowfish@gmail.com
[4D_Cubing] wrote:

OK. Given that, I'd say that:

1-5 are primitive.

7-8 are canonical.=C2=A0iv>

(The rest of ROIL (as in,
other twists of the centre 2x2x2 and the
restacked IO twists) may be canonical or
may require labeling. I am unsure.) =C2=A0<=
/div>

6&9(&10?) only
with clear labeling (ie. counted as a
separate kind of solve, like macro vs
non-macro in MC4D). 11 could possibly be
included at a stretch.

12 is unacceptable.=C2=A0div>

~Luna

>

On 6 Jan 2018
01:45, "Melinda Green href=3D"mailto:melinda@superliminal.c=
om"
target=3D"_blank"
moz-do-not-send=3D"true">melinda@supe=
rliminal.com
[4D_Cubing]" < href=3D"mailto:4D_Cubing@yahoogroups.=
.com"
target=3D"_blank"
moz-do-not-send=3D"true">4D_Cubing@ya=
hoogroups.com>
wrote:

class=3D"m_8311926157861543071quote"
style=3D"border-left:1px #ccc solid">

=C2=A0
id=3D"m_8311926157861543071m_1161=
542213992904350ygrp-mlmsg">
id=3D"m_8311926157861543071m_11=
61542213992904350ygrp-msg">
id=3D"m_8311926157861543071m_=
1161542213992904350ygrp-text">

Certainly.



#4 is a twist of the
central 2x2x2 block
about the long axis. It
is a twist of the face
joining the two halves
of the puzzle. It is
equivalent to twisting
both end caps the
opposite direction.



#5 is the first
"compound move" that I
talk about in the video
href=3D"https://www.youtu=
be...com/watch?v=3D_D4m1Kit3TI&t=3D1m39s"
target=3D"_blank"
moz-do-not-send=3D"true">=
here
as a natural consequence
of combining simple
rotations with 90 degree
twists.



#7 is the fancy 4D
change of projection
described in the first
link in the description
href=3D"https://www.youtu=
be.com/watch?v=3Dd2Fh_1m0UVY"
target=3D"_blank"
moz-do-not-send=3D"true">=
here.



-Melinda

class=3D"m_8311926157861543=
071elided-text">



class=3D"m_83119261578615=
43071m_1161542213992904350moz-cite-prefix">On
1/5/2018 9:54 AM, Luna
Pe=C3=B1a class=3D"m_8311926157861543071m_1161542213992904350moz-txt-link-abbreviated=
"
href=3D"mailto:scarecrowfish@gmail.com" target=3D"_blank"
moz-do-not-send=3D"true=
">scarecrowfish@gmail.com
[4D_Cubing] wrote:

Can I
get clearer
definitions of 4, 5
and 7?

~Luna=

class=3D"gmail_extra"><=
br>
class=3D"gmail_quote"=
>On
4 Jan 2018 23:28,
"Melinda Green href=3D"mailto:melinda@superliminal.com" target=3D"_blank"
moz-do-not-send=3D"=
true">melinda@superliminal.com
[4D_Cubing]" <href=3D"mailto:4D_Cubing@yahoogroups.com" target=3D"_blank"
moz-do-not-send=3D"=
true">4D_Cubing@yahoogroups.com>
wrote: type=3D"attribution=
">
class=3D"gmail_quot=
e"
style=3D"border-left:1px #ccc solid">
style=3D"backgrou=
nd-color:#fff">
=C2=A0n>
id=3D"m_8311926157861543071m_1161542213992904350m_-6533444127507305308ygrp-=
mlmsg">
id=3D"m_8311926157861543071m_1161542213992904350m_-6533444127507305308ygrp-=
msg">
id=3D"m_8311926157861543071m_1161542213992904350m_-6533444127507305308ygrp-=
text">

First off,
please check
out href=3D"https://w=
ww.youtube..com/watch?v=3DfYxn4wPe2ZE"
target=3D"_blank" moz-do-not-send=3D"true">Zander Bolgar's lovely solution
video that
he invited me
to share. It's
very cool to
see someone
developing
something like
finger tricks
and blasting
through a
solution. It's
very much like
href=3D"https://groups.yahoo.com/neo/groups/4D_Cubing/conversations/topics/=
3803"
target=3D"_blank" moz-do-not-send=3D"true">Bob's and href=3D"https://groups.yahoo.com/neo/groups/4D_Cubing/conversations/message=
s/3904"
target=3D"_blank" moz-do-not-send=3D"true">Joel's solutions as well as =
href=3D"https://www.youtube.com/watch?v=3DpKHU5sFaGvY" target=3D"_blank"
moz-do-not-send=
=3D"true">Marc's
approach.



This makes for
a great
launching
point for
questions
about which
moves should
be included in
a canonical
set. Of course
any move that
results in a
reachable
state can be
justified in a
solution, but
there's such a
spectrum from
"obviously
fine" to
"obviously
not".=C2=A0 Now
that we've
gotten some
experience
with this
puzzle and the
practicalities
of solving it,
I feel it's
time to see if
we can find
some sort of
natural
canonical set,
so I'd love to
hear your
thoughts.



Here is the
list of moves
I know about,
loosely
ordered as
described
above:

1. Simple
   rotations


2. 90 degree
   twists of
   outer face


3. 180
   degree twists
   of side face


4. Center
   face axial
   twist


5. Arbitrary
   half-puzzle
   juxtapositionsi>
   
6. Clamshell
   move


7. 
   Whole-puzzle
   reorientationsi>
   
8. 90 degree
   twist of side
   face (each
   2x2x1 square
   rotate in
   opposite
   directions)
   
   


9. Single
   end cap twist
   (with parity
   restrictions?)
   [fine for
   scrambling]


10. 
    Restacking
    moves [fine
    for
    scrambling]


11. Single
    piece flip


12. Reassemble
    entire puzzle
    
    

I suspect the
trickiest part
has to do with
#9 which is
the one I
would most
like to nail
down.



I intend to
create a
follow-up
video to talk
about all of
these and any
others you can
think of. The
way you can
help is to
offer
additions and
corrections to
the above
list, and
especially in
suggesting
ways to
reorder it.
Then please
suggest where
you'd draw
three lines:

• Everything
  above is
  primitive (Or
  "basic" or
  "elementary"
  as Joel calls
  them)


• Everything
  above is
  canonical. IE
  always
  acceptable in
  solutions


• Nothing
  below is
  acceptable in
  solutions.

Thanks all!

-Melinda

class=3D"m_831192615786154307=
1elided-text">

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I hadn't seen that, or at least I forgot about it.
I still think it needs labeling though, because you could just do the 180
twists instead.

This matters, because doing the clamshell would cut down on times, and I
think any sort of shortcut like that should be kept separate. The physical
move count of a speedsolve should equal the virtual twist count of the same
scramble, and a clamshell would be one physical move for three virtual
moves.

The R L moves are ok because you still have to physically do both twists.
It's essentially a fingertrick.

(I'm thinking more about speedsolving than fewest moves)

~Luna

On 6 Jan 2018 02:43, "Melinda Green melinda@superliminal.com [4D_Cubing]" <
4D_Cubing@yahoogroups.com> wrote:

>
>
> #6 is equivalent to three simple 180 degree twists like I demonstrated
> here .
> -Melinda
>
> On 1/5/2018 6:35 PM, Luna Pe=C3=B1a scarecrowfish@gmail.com [4D_Cubing] w=
rote:
>
> I see 5 as the equivalent of doing R L on a 2^3, which is obviously just
> two twists. However, it is not as obvious to me how 6 is simple twists.
> Perhaps when I get my puzzle and see exactly what it does to the puzzle,
> I'll change my mind, but I would only class moves that are simple on both
> the physical and virtual puzzle as primitive.
>
> ~Luna
>
> On 6 Jan 2018 02:32, "Melinda Green melinda@superliminal.com [4D_Cubing]"
> <4D_Cubing@yahoogroups.com> wrote:
>
>
>
> That's very helpful, Luna, but I'm curious: Why do you see #5 as primitiv=
e
> but not #6? Seems to me like it should be both or neither.
> -Melinda
>
>
> On 1/5/2018 6:07 PM, Luna Pe=C3=B1a scarecrowfish@gmail.com [4D_Cubing] w=
rote:
>
> OK. Given that, I'd say that:
>
> 1-5 are primitive.
>
> 7-8 are canonical.
>
> (The rest of ROIL (as in, other twists of the centre 2x2x2 and the
> restacked IO twists) may be canonical or may require labeling. I am
> unsure.)
>
> 6&9(&10?) only with clear labeling (ie. counted as a separate kind of
> solve, like macro vs non-macro in MC4D). 11 could possibly be included at=
a
> stretch.
>
> 12 is unacceptable.
>
> ~Luna
>
> On 6 Jan 2018 01:45, "Melinda Green melinda@superliminal.com [4D_Cubing]"
> <4D_Cubing@yahoogroups.com <4D_Cubing@yahoogroups..com>> wrote:
>
>
>
> Certainly.
>
> #4 is a twist of the central 2x2x2 block about the long axis. It is a
> twist of the face joining the two halves of the puzzle. It is equivalent =
to
> twisting both end caps the opposite direction.
>
> #5 is the first "compound move" that I talk about in the video here
> as a natural
> consequence of combining simple rotations with 90 degree twists.
>
> #7 is the fancy 4D change of projection described in the first link in th=
e
> description here .
>
> -Melinda
>
>
> On 1/5/2018 9:54 AM, Luna Pe=C3=B1a scarecrowfish@gmail.com [4D_Cubing] w=
rote:
>
> Can I get clearer definitions of 4, 5 and 7?
>
> ~Luna
>
> On 4 Jan 2018 23:28, "Melinda Green melinda@superliminal.com [4D_Cubing]"
> <4D_Cubing@yahoogroups.com> wrote:
>
>>
>>
>> First off, please check out Zander Bolgar's lovely solution video
>> that he invited me to
>> share. It's very cool to see someone developing something like finger
>> tricks and blasting through a solution. It's very much like Bob's
>> >
>> and Joel's
>> 04>
>> solutions as well as Marc's vY>
>> approach.
>>
>> This makes for a great launching point for questions about which moves
>> should be included in a canonical set. Of course any move that results i=
n a
>> reachable state can be justified in a solution, but there's such a spect=
rum
>> from "obviously fine" to "obviously not". Now that we've gotten some
>> experience with this puzzle and the practicalities of solving it, I feel
>> it's time to see if we can find some sort of natural canonical set, so I=
'd
>> love to hear your thoughts.
>>
>> Here is the list of moves I know about, loosely ordered as described
>> above:
>>
>> 1. Simple rotations
>> 2. 90 degree twists of outer face
>> 3. 180 degree twists of side face
>> 4. Center face axial twist
>> 5. Arbitrary half-puzzle juxtapositions
>> 6. Clamshell move
>> 7. Whole-puzzle reorientations
>> 8. 90 degree twist of side face (each 2x2x1 square rotate in opposite
>> directions)
>> 9. Single end cap twist (with parity restrictions?) [fine for
>> scrambling]
>> 10. Restacking moves [fine for scrambling]
>> 11. Single piece flip
>> 12. Reassemble entire puzzle
>>
>> I suspect the trickiest part has to do with #9 which is the one I would
>> most like to nail down.
>>
>> I intend to create a follow-up video to talk about all of these and any
>> others you can think of. The way you can help is to offer additions and
>> corrections to the above list, and especially in suggesting ways to reor=
der
>> it. Then please suggest where you'd draw three lines:
>>
>> - Everything above is primitive (Or "basic" or "elementary" as Joel
>> calls them)
>> - Everything above is canonical. IE always acceptable in solutions
>> - Nothing below is acceptable in solutions.
>>
>> Thanks all!
>> -Melinda
>>
>
>
>
>
>
>=20
>

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