--Apple-Mail=_A38EB000-F067-4C06-BDAE-852C218D1CE0
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This is really cool. I hadn=92t heard of =91super=92 and =91multi=92 before=
, but it always bothered me that the =91solved=92 3x3x3 could actually have=
the face centers rotated relative to how they were before. For this reason=
I prefer 3x3x3 cubes with images on them, so that this degeneracy is broke=
n and the parameter space increases.=20
But this technique of projecting parts of the inner faces on the outside of=
the cube using spherical cuts is a much more pleasing way of breaking this=
degeneracy than adding some company logo to the cube. Can one purchase the=
se?
Still, for the 3x3x3x3, could one break the degeneracy just as well as the =
spherification you suggest just by putting images on all the cubies? I gues=
s that wouldn=92t be enough to expose the 2x2x2x2 core of a 4x4x4x4, but wo=
uld it be enough for the 3x3x3x3 since the 1x1x1x1 doesn=92t scramble anywa=
y?
Also, just a point of clarification, you say the center hypercubie can=92t =
be scrambled anyway on the super multi 3x3x3x3, but this doesn=92t mean the=
super multi 3x3x3x3 is the same to solve as the normal 3x3x3x3- the super =
multi version does break some degeneracies and increase the number of unsol=
ved states of the puzzle, correct?
Best,
Dave
PS. Are you a member of this list Carl? This twisty puzzle website seems ne=
at. Does it predate MC4D?
On Jul 23, 2016, at 1:30 PM, carl.n.hoff@gmail.com [4D_Cubing] <4D_Cubing@y=
ahoogroups.com> wrote:
>=20
> Better here is very subjective. I just really like playing with Super and=
Multi puzzles and the current 3x3x3x3 is neither.=20=20
>=20
>=20
>=20
> Let's take a quick look at the current 3x3x3x3.
>=20
> http://wwwmwww.com/3x3x3x3/3x3x3x3.gif
>=20
> There is an excellent video that explains it very well here that I'd high=
ly recommend.
>=20
> https://youtu.be/yhPH1369OWc
>=20
> So here I will just cover some of the basics.
>=20
>=20
>=20
> This puzzle exists in 4D space. In addition to the x, y, and z directions=
we also have the w direction.
>=20
>=20
>=20
> The positive X direction is what we call Right and I'll color stickers on=
that face/cell Red.
>=20
> The negative X direction is what we call Left and I'll color stickers on =
that face/cell Orange.
>=20
>=20
>=20
> The positive Y direction is what we call Forward and I'll color the stick=
ers on that face/cell Blue.
>=20
> The negative Y direction is what we call Backward and I'll color the stic=
kers on that face/cell Green.
>=20
>=20
>=20
> The positive Z direction is what we call Up and I'll color the stickers o=
n that face/cell Yellow.
>=20
> The negative Z direction is what we call Down and I'll color the stickers=
on that face/cell White.
>=20
>=20
>=20
> The positive W direction is called the Ana direction and I'll color the s=
tickers on that face/cell Magenta.
>=20
> The negative W direction is called the Kata direction and I'll color the =
stickers on that face/cell Cyan.
>=20
>=20
>=20
> The cell with the White stickers is missing from this image and is the 8t=
h cell. It can be placed below Down, above Up, to the right of Right, to t=
he left of Left, in front of Front, or behind the Back. In truth it is act=
ually in all these locations at the same time.
>=20
>=20
>=20
> So for a 3x3x3x3 we would expect to find 81 different hypercubies. In th=
is post Brandon discussed them all. But suffice it to say we have:
>=20
>=20
>=20
> 8 pieces which correspond to cell centers and they are only marked with a=
single sticker.
>=20
> 24 pieces which correspond to cell faces and they are marked with 2 stick=
ers.
>=20
> 32 pieces which correspond to cell edges and they are marked with 3 stick=
ers.
>=20
> 16 pieces which correspond to cell corners and they are marked with 4 sti=
ckers.
>=20
>=20
>=20
> This comes to 80 pieces and we were expecting 81. So we are missing one.=
So this is NOT a Multi puzzle. And where is the missing piece?
>=20
>=20
>=20
> Let's check to see if its a Super puzzle. In a Super 3x3x3x3 each piece =
would need a fixed position and orientation in the solved state.
>=20
>=20
>=20
> Each cell center can reach 24 possible orientations. With just a single =
sticker we cannot distinguish any of these orientations. So that alone mea=
ns this is not a Super puzzle. But let's also look at the cell faces. The=
se contain just 2 stickers which are from neighboring cells. These 2 stick=
ers contain enough orientation information to reduce the ambiguity in the p=
ossible orientations by a factor of 6 but that still leaves 4 possible orie=
ntations that it could be in and still appear solved. So the cell faces al=
so keep this from being a Super 3x3x3x3.
>=20
>=20
>=20
> Both the cell edges and the cell corners already contain enough informati=
on to give them a unique position and orientation in the solved state.
>=20
>=20
>=20
> Can we do better? Can we make a Super Multi 3x3x3x3?=20=20
>=20
>=20
>=20
> Well before we answer that let's see what we need to do to make a Super M=
ulti 3x3x3.
>=20
>=20
>=20
> Here is your normal 3x3x3.
>=20
> http://wwwmwww.com/3x3x3x3/Rubiks.png
>=20
> And let's look at an exploded view.
>=20
> http://wwwmwww.com/3x3x3x3/RubiksExp.png
>=20
>=20
>=20
> This view allows us to see all 3x3x3 or 27 cubies of the 3x3x3. As was t=
he case with the 3x3x3x3 there is one that is missing any stickers. This i=
s the core cubie and keeps the normal 3x3x3 from being a Multi puzzle. Als=
o the face cubies are only marked with a single sticker and this does not p=
rovide enough information to distinguish between its 4 possible orientation=
s. So the normal 3x3x3 is also not a Super puzzle.
>=20
>=20
>=20
> But we do know a way to make a Super Multi (aka Real) 3x3x3. We call it =
the Circle Cube. So let's examine how it pulled that off.
>=20
> http://wwwmwww.com/3x3x3x3/CircleCube.gif
>=20
> Now let's look at an exploded view of this puzzle.
>=20
> http://wwwmwww.com/3x3x3x3/CircleCubeExp.png
>=20
> Here we see how all the stickers map to the 27 cubies. Let's look at the=
m in turn.
>=20
>=20
>=20
> Here is the core cubie. It now has stickers on ALL 6 faces.
>=20
> http://wwwmwww.com/3x3x3x3/CircleCubeCore.png
>=20
>=20
>=20
> Here is a face cubie. This now has stickers on 4 of its 6 faces and now c=
ontains the information needed for solving its orientation.
>=20
> http://wwwmwww.com/3x3x3x3/CircleCubeFace.png
>=20
>=20
>=20
> Here is the edge cubie. It now has stickers on 4 of its 6 faces as well.
>=20
> http://wwwmwww.com/3x3x3x3/CircleCubeEdge.png
>=20
>=20
>=20
> And here is the corner cubie. It has maintained the 3 stickers that it or=
iginally had.
>=20
> http://wwwmwww.com/3x3x3x3/CircleCubeCorner.png
>=20
>=20
>=20
> So... we know its possible to make a Super Multi 3x3x3x3. Can we do the =
same thing to the 3x3x3x3? If so how?
>=20
>=20
>=20
> Well the answer is yes... and I'll show you how. Instead of adding circu=
lar cuts to the faces, we need to add spherical cuts to the cells. And thi=
s is what the Super Multi 3x3x3x3 (or Sphere HyperCube) looks like.
>=20
> http://wwwmwww.com/3x3x3x3/Sphere3x3x3x3.gif
>=20
> Just as the circle is fixed in the Circle Cube while the rest of the laye=
r rotates about it, the sphere is fixed while the rest of the cell is rotat=
ed about it.
>=20
>=20
>=20
> And just as you can interpret the circles on the faces of a Circle Cube a=
s windows that allow you the see the layer below, the same is true for thes=
e spheres on the cells of the 3x3x3x3. We can now look though these window=
s and see many of the previously unstickered cubes=AB of the 81 hyper-cubie=
s that make up the 3x3x3x3.=20
>=20
>=20
>=20
> So now let's look at the individual piece types.
>=20
>=20
>=20
> Here is the Core of the 3x3x3x3. It is totally unseen in the standard pi=
cture but it now has all 8 cubes stickered. The White sticker is in the 8t=
h cell off screen.
>=20
> http://wwwmwww.com/3x3x3x3/Sphere3x3x3x3Core.png
>=20
>=20
>=20
> Here is a Cell Center. It now has 6 of the 8 possible stickers and now ha=
s a unique position and orientation in the solved state. Just was with the =
Face Centers on the Circle Cube, the Cell Centers do not have a sticker in =
the cell they represent. And the other missing sticker is from the opposit=
e cell.
>=20
> http://wwwmwww.com/3x3x3x3/Sphere3x3x3x3CellCenter.png
>=20
>=20
>=20
> Here is the Cell Face. It too now has 6 of the 8 possible stickers and ha=
s a unique position and orientation in the solved state.
>=20
> http://wwwmwww.com/3x3x3x3/Sphere3x3x3x3CellFace.png
>=20
>=20
>=20
> Here is a Cell Edge. It goes from having 3 stickers to having 5 of its 8=
possible stickers.
>=20
> http://wwwmwww.com/3x3x3x3/Sphere3x3x3x3CellEdge.png
>=20
>=20
>=20
> And finally here is the Cell Corner. It gains no new stickers but it alre=
ady had enough to give it a unique position and orientation in the solved s=
tate.
>=20
> http://wwwmwww.com/3x3x3x3/Sphere3x3x3x3CellCorner.png
>=20
>=20
>=20
> So we have now made the Super Multi (aka Real) 3x3x3x3.
>=20
>=20
>=20
> You may say that is an awful lot of work to expose a core that can never =
be scrambled anyways. And yes... that is true for the 3x3x3x3. But this m=
ethod has implications that go FAR beyond the 3x3x3x3 itself. We can now m=
ake a Sphere 4x4x4x4 and not only would it allow you to solve the 2x2x2x2 o=
n the inside but it would also be able to give the 2-sticker face pieces a =
unique position as well. So you can make a Super Multi 4x4x4x4. I believe=
you can make a Double Sphere 5x5x5x5 which would map to the Super Multi 5x=
5x5x5 and if so that could in turn be used to make the Complex 3x3x3x3. An=
d you can even take this in different directions. If we allow some of the =
spheres to rotate with their cell but not all we will then have the Crazy P=
lus 3x3x3x3's that we can play with. This enables all sorts of possibiliti=
es...
>=20
>=20
>=20
> Now to see if I can figure out how to post this to the MC4D Yahoo Group..=
.
>=20
>=20
>=20
> Enjoy,
>=20
> Carl
>=20
>=20
>=20
>=20
> =AB I was tempted to say "cells" here but cell is already being used for=
the 8 faces/cells of the 3x3x3x3. I didn't think "faces" was appropriate =
as that implies 2D squares and the faces of a hyper-cube are cubes. So I h=
ave used the term "cubes" but "the previously unstickered cubes of the hype=
r-cubies" sounds very odd to me. Is there a better term? In 3D I would say=
sides of the cubies. Is "sides" a better term to use here as well?
>=20
>=20
>=20
>=20
>=20
--Apple-Mail=_A38EB000-F067-4C06-BDAE-852C218D1CE0
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html;
charset=windows-1252
ine-height: 1.22em; margin: 0px 0px 1em;">Better here is very subjective. I=
just really like playing with <=
/span>rvandeventer.nl/index.php/Super-(puzzle_name)" style=3D"line-height: 1.22em=
; font-family: Verdana;">Super andpace"> stypedia.oskarvandeventer.nl/index.php/Multi-(puzzle_name)" style=3D"line-h=
eight: 1.22em; font-family: Verdana;">Multi puzzles and the curren=
t 3x3x3x3 is neither.
x 0px 1em;">
1.22em; margin: 0px 0px 1em;">Let's take a quick look at the current 3x3x3=
x3.
">There is an excellent video that explains it very well here that I'd high=
ly recommend.
rel=3D"nofollow" target=3D"_blank" href=3D"https://youtu.be/yhPH1369OWc" st=
yle=3D"line-height: 1.22em; font-family: Verdana;">https://youtu.be/yhPH136=
9OWc
So here =
I will just cover some of the basics.
argin: 0px 0px 1em;">
e-height: 1.22em; margin: 0px 0px 1em;">This puzzle exists in 4D space. In =
addition to the x, y, and z directions we also have the w direction.
The =
positive X direction is what we call Right and I'll color stickers on that =
face/cell Red.
Th=
e negative X direction is what we call Left and I'll color stickers on that=
face/cell Orange.
">
argin: 0px 0px 1em;">The positive Y direction is what we call Forward and I=
'll color the stickers on that face/cell Blue.
ne-height: 1.22em; margin: 0px 0px 1em;">
>
The positive Z =
direction is what we call Up and I'll color the stickers on that face/cell =
Yellow.
The negat=
ive Z direction is what we call Down and I'll color the stickers on that fa=
ce/cell White.
n: 0px 0px 1em;">The positive W direction is called the Ana direction and I=
'll color the stickers on that face/cell Magenta.
t: 1.22em; margin: 0px 0px 1em;">The negative W direction is called the Kat=
a direction and I'll color the stickers on that face/cell Cyan.
=3D"line-height: 1.22em; margin: 0px 0px 1em;">
22em;">
The cell =
with the White stickers is missing from this image and is the 8th cell. &nb=
sp;It can be placed below Down, above Up, to the right of Right, to the lef=
t of Left, in front of Front, or behind the Back. In truth it is actu=
ally in all these locations at the same time.
.22em; margin: 0px 0px 1em;">
e=3D"line-height: 1.22em; margin: 0px 0px 1em;">So for a 3x3x3x3 we would e=
xpect to find 81 different hypercubies. In thisonverted-space"> http://www.twistypuzzles.com/forum/viewtopic.php?p=3D351831#p351831" style=
=3D"line-height: 1.22em; font-family: Verdana;">post Brandon discu=
ssed them all. But suffice it to say we have:
ght: 1.22em; margin: 0px 0px 1em;">
height: 1.22em; margin: 0px 0px 1em;">32 pieces which correspond to cell ed=
ges and they are marked with 3 stickers.
; margin: 0px 0px 1em;">16 pieces which correspond to cell corners and they=
are marked with 4 stickers.
x 0px 1em;">
1.22em; margin: 0px 0px 1em;">This comes to 80 pieces and we were expectin=
g 81. So we are missing one. So this is NOT a Multi puzzle. &nb=
sp;And where is the missing piece?
in: 0px 0px 1em;">
eight: 1.22em; margin: 0px 0px 1em;">Let's check to see if its a Super puzz=
le. In a Super 3x3x3x3 each piece would need a fixed position and ori=
entation in the solved state.
px 0px 1em;">
: 1.22em; margin: 0px 0px 1em;">Each cell center can reach 24 possible orie=
ntations. With just a single sticker we cannot distinguish any of the=
se orientations. So that alone means this is not a Super puzzle. &nbs=
p;But let's also look at the cell faces. These contain just 2 sticker=
s which are from neighboring cells. These 2 stickers contain enough o=
rientation information to reduce the ambiguity in the possible orientations=
by a factor of 6 but that still leaves 4 possible orientations that it cou=
ld be in and still appear solved. So the cell faces also keep this fr=
om being a Super 3x3x3x3.
px 1em;">
22em; margin: 0px 0px 1em;">Both the cell edges and the cell corners alread=
y contain enough information to give them a unique position and orientation=
in the solved state.
em;">
; margin: 0px 0px 1em;">Can we do better? Can we make a Super Multi 3x3x3x3=
?
e=3D"line-height: 1.22em;">
0px 1em;">Well before we answer that let's see what we need to do to make =
a Super Multi 3x3x3.
m;">
margin: 0px 0px 1em;">Here is your normal 3x3x3.
t: 1.22em; margin: 0px 0px 1em;">=3D"http://wwwmwww.com/3x3x3x3/Rubiks.png" style=3D"line-height: 1.22em; fo=
nt-family: Verdana;">http://wwwmwww.com/3x3x3x3/Rubiks.png
=3D"line-height: 1.22em; margin: 0px 0px 1em;">And let's look at an explode=
d view.
0px 1em;">
.22em; margin: 0px 0px 1em;">This view allows us to see all 3x3x3 or 27 cub=
ies of the 3x3x3. As was the case with the 3x3x3x3 there is one that =
is missing any stickers. This is the core cubie and keeps the normal =
3x3x3 from being a Multi puzzle. Also the face cubies are only marked=
with a single sticker and this does not provide enough information to dist=
inguish between its 4 possible orientations. So the normal 3x3x3 is a=
lso not a Super puzzle.
1em;">
em; margin: 0px 0px 1em;">But we do know a way to make a Super Multi (aka R=
eal) 3x3x3. We call it the Circle Cube. So let's examine how it=
pulled that off.
margin: 0px 0px 1em;">Now let's look at an exploded view of this puzzle.>
x 1em;">Here we see how all the stickers map to the 27 cubies. Let's =
look at them in turn.
em;">
; margin: 0px 0px 1em;">Here is the core cubie. It now has stickers o=
n ALL 6 faces.
leCubeCore.png" style=3D"line-height: 1.22em; font-family: Verdana;">http:/=
/wwwmwww.com/3x3x3x3/CircleCubeCore.png
2em; margin: 0px 0px 1em;">
=3D"line-height: 1.22em; margin: 0px 0px 1em;">Here is a face cubie. This n=
ow has stickers on 4 of its 6 faces and now contains the information needed=
for solving its orientation.
ine-height: 1.22em; margin: 0px 0px 1em;">
">
Here is the ed=
ge cubie. It now has stickers on 4 of its 6 faces as well.
ine-height: 1.22em; margin: 0px 0px 1em;">ank" href=3D"http://wwwmwww.com/3x3x3x3/CircleCubeEdge.png" style=3D"line-h=
eight: 1.22em; font-family: Verdana;">http://wwwmwww.com/3x3x3x3/CircleCube=
Edge.png
style=3D"line-height: 1.22em;">
0px 0px 1em;">And here is the corner cubie. It has maintained the 3 sticke=
rs that it originally had.
line-height: 1.22em; margin: 0px 0px 1em;">
;">
So... we know=
its possible to make a Super Multi 3x3x3x3. Can we do the same thing=
to the 3x3x3x3? If so how?
n: 0px 0px 1em;">
ight: 1.22em; margin: 0px 0px 1em;">Well the answer is yes... and I'll show=
you how. Instead of adding circular cuts to the faces, we need to ad=
d spherical cuts to the cells. And this is what the Super Multi 3x3x3=
x3 (or Sphere HyperCube) looks like.
rgin: 0px 0px 1em;">wmwww.com/3x3x3x3/Sphere3x3x3x3.gif" style=3D"line-height: 1.22em; font-fam=
ily: Verdana;">http://wwwmwww.com/3x3x3x3/Sphere3x3x3x3.gif
=3D"line-height: 1.22em; margin: 0px 0px 1em;">Just as the circle is fixed =
in the Circle Cube while the rest of the layer rotates about it, the sphere=
is fixed while the rest of the cell is rotated about it.
ne-height: 1.22em; margin: 0px 0px 1em;">
>
And just as you=
can interpret the circles on the faces of a Circle Cube as windows that al=
low you the see the layer below, the same is true for these spheres on the =
cells of the 3x3x3x3. We can now look though these windows and see ma=
ny of the previously unstickered cubesont-size: 16pt; font-family: Wingdings; color: red;">=AB of the=
81 hyper-cubies that make up the 3x3x3x3.
: 1.22em; margin: 0px 0px 1em;">
tyle=3D"line-height: 1.22em; margin: 0px 0px 1em;">So now let's look at the=
individual piece types.
x 1em;">
2em; margin: 0px 0px 1em;">Here is the Core of the 3x3x3x3. It is tot=
ally unseen in the standard picture but it now has all 8 cubes stickered. &=
nbsp;The White sticker is in the 8th cell off screen.
eight: 1.22em; margin: 0px 0px 1em;">href=3D"http://wwwmwww.com/3x3x3x3/Sphere3x3x3x3Core.png" style=3D"line-hei=
ght: 1.22em; font-family: Verdana;">http://wwwmwww.com/3x3x3x3/Sphere3x3x3x=
3Core.png
: 0px 0px 1em;">Here is a Cell Center. It now has 6 of the 8 possible stick=
ers and now has a unique position and orientation in the solved state. Just=
was with the Face Centers on the Circle Cube, the Cell Centers do not have=
a sticker in the cell they represent. And the other missing sticker =
is from the opposite cell.
height: 1.22em;">
>Here is the Cell Face. It too now has 6 of the 8 possible stickers and has=
a unique position and orientation in the solved state.
-height: 1.22em; margin: 0px 0px 1em;">" href=3D"http://wwwmwww.com/3x3x3x3/Sphere3x3x3x3CellFace.png" style=3D"li=
ne-height: 1.22em; font-family: Verdana;">http://wwwmwww.com/3x3x3x3/Sphere=
3x3x3x3CellFace.png
1em;">
em; margin: 0px 0px 1em;">Here is a Cell Edge. It goes from having 3 =
stickers to having 5 of its 8 possible stickers.
: 1.22em; margin: 0px 0px 1em;">=3D"http://wwwmwww.com/3x3x3x3/Sphere3x3x3x3CellEdge.png" style=3D"line-hei=
ght: 1.22em; font-family: Verdana;">http://wwwmwww.com/3x3x3x3/Sphere3x3x3x=
3CellEdge.png
>
rgin: 0px 0px 1em;">And finally here is the Cell Corner. It gains no new st=
ickers but it already had enough to give it a unique position and orientati=
on in the solved state.
So=
we have now made the Super Multi (aka Real) 3x3x3x3.
eight: 1.22em; margin: 0px 0px 1em;">
>
You may say that is=
an awful lot of work to expose a core that can never be scrambled anyways.=
And yes... that is true for the 3x3x3x3. But this method has i=
mplications that go FAR beyond the 3x3x3x3 itself. We can now make a =
Sphere 4x4x4x4 and not only would it allow you to solve the 2x2x2x2 on the =
inside but it would also be able to give the 2-sticker face pieces a unique=
position as well. So you can make a Super Multi 4x4x4x4. I bel=
ieve you can make a Double Sphere 5x5x5x5 which would map to the Super Mult=
i 5x5x5x5 and if so that could in turn be used to make the Complex 3x3x3x3.=
And you can even take this in different directions. If we allo=
w some of the spheres to rotate with their cell but not all we will then ha=
ve the Crazy Plus 3x3x3x3's that we can play with. This enables all s=
orts of possibilities...
x 1em;">
2em; margin: 0px 0px 1em;">Now to see if I can figure out how to post this =
to the MC4D Yahoo Group...
0px 1em;">
.22em; margin: 0px 0px 1em;">Enjoy,
gin: 0px 0px 1em;">Carl
1em;">
margin: 0px 0px 1em;">;">font-size: 16pt; word-spacing: normal; font-weight: 400;">=AB <=
/span> I was tempted to say "cells" here but cell is already being use=
d for the 8 faces/cells of the 3x3x3x3. I didn't think "faces" was ap=
propriate as that implies 2D squares and the faces of a hyper-cube are cube=
s. So I have used the term "cubes" but "the previously unstickered cu=
bes of the hyper-cubies" sounds very odd to me. Is there a better term? &nb=
sp;In 3D I would say sides of the cubies. Is "sides" a better term to use h=
ere as well?
ght: 1.22em;">
--------------EA1A59ED3E0F4E3789D85EE2
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Content-Transfer-Encoding: quoted-printable
Don Hatch has written a software solution=20
puzzles with a layered approach a little like you describe though it=20
uses only a couple of simple algorithms since that's all that is needed.=20
His input format is especially elegant and seems to relate to your next=20
subject.
Regarding Menger cubes, have you seen this=20
it on the list when it first appeared. We wondered whether it could be a=20
design for a real fractal twisty puzzle but I don't think we came to any=20
conclusion.
Do try Magic Tile. It is special in that it is as much a work of art as=20
it is a puzzle engine. I can easily become mesmerized watching it=20
auto-solve.
-Melinda
On 7/21/2016 2:02 PM, llamaonacid@gmail.com [4D_Cubing] wrote:
>
>
> I been wondering that a Rubik's Cube with more than 7D would not be=20
> difficult but tedious to solve. If it ever gets created whether you=20
> see pieces or stickers I have come up with two ideas to make it more=20
> fun. One is to change the objective of the game and rather than trying=20
> to solve it users find commutators for each d-dimensional Rubik's Cube=20
> in the program. It would also be nice to have something I call=20
> commutator bank where everyone can share their commutators and as a=20
> result it becomes easier to find the most efficient commutators.=20
> Another way to make it less tedious would be to change it to a level 1=20
> Merger sponge in higher dimensions. For that all you have to do is=20
> leave the two types of pieces with the highest colors. So in 5D all=20
> you work with is 4 and 5 color pieces.
>
> Another idea that I came up with is a level 1 of a 3x3x3 or even a=20
> level 2 Merger sponge of a 9x9x9 Rubik Cube. I wonder if the number of=20
> possible states would increase if you can can tw irl one 2c piece in=20
> the level 1 of a 3x3x3 so that you change the position of the two=20
> colors with each other. If the number of possible states decrease with=20
> this new twirling move it means the puzzle becomes easier to solve and=20
> that is not what I want.
>
> Anyways, those are just random thoughts I been having and I do not=20
> know if those ideas are good or bad. Maybe I will try Magic Tile but I=20
> like n-cubes the most.
>
>=20
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I been wondering that a Rubik's Cube with more than 7D would not
be difficult but tedious to solve. If it ever gets created whether
you see pieces or stickers I have come up with two ideas to make
it more fun. One is to change the objective of the game and rather
than trying to solve it users find commutators for each
d-dimensional Rubik's Cube in the program. It would also be nice
to have something I call commutator bank where everyone can share
their commutators and as a result it becomes easier to find the
most efficient commutators. Another way to make it less tedious
would be to change it to a level 1 Merger sponge in higher
dimensions. For that all you have to do is leave the two types of
pieces with the highest colors. So in 5D all you work with is 4
and 5 color pieces.
Another idea that I came up with is a level 1 of a 3x3x3 or even a
level 2 Merger sponge of a 9x9x9 Rubik Cube. I wonder if the
number of possible states would increase if you can can tw irl one
2c piece in the level 1 of a 3x3x3 so that you change the position
of the two colors with each other. If the number of possible
states decrease with this new twirling move it means the puzzle
becomes easier to solve and that is not what I want.
Anyways, those are just random thoughts I been having and I do not
know if those ideas are good or bad. Maybe I will try Magic Tile
but I like n-cubes the most.
=20=20=20=20=20=20
Hello David, =C2= All of these are Super-Multi puzzles. It is t= Also note I'm just talking about the 3x3x3x3 here.=C2=A0 The S= And I've been a member of MC4= I'm sad to say I'm not familiar with the or= Carl
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This was an intriguing thread to follow! After reading it, I added some
circle puzzles to MagicTile. However, they don't match the behavior of the
physical puzzles unless you artificially limit slicemask usage to only
allow 2nd layer twists. I added a circle cube and a circle Megaminx, but
also a circle Klein quartic, which I thought justified this post. When
limited to 2nd layer twists, I think the circle KQ can represent a "super
multi Klein quartic", and it's cool to think about a hidden 24-color
genus-3 "cubie" :)
Roice
On Wed, Jul 27, 2016 at 8:54 PM, Dave Reens dave.reens@gmail.com
[4D_Cubing] <4D_Cubing@yahoogroups.com> wrote:
>
>
> Hello Carl,
>
> Thanks a lot for all the great information and links. I'm definitely
> adding the 3x3x3 circle to my wish list, and maybe someday when I'm rich
> I'll have to buy your 5x5x5 with the double circle :-), what an awesome
> creation.
>
> Dave
>
> On Jul 24, 2016, at 4:48 PM, carl.n.hoff@gmail.com [4D_Cubing] <
> 4D_Cubing@yahoogroups.com> wrote:
>
>
>
> Hello David,
>
> The use of the word Super in this context has been around since the
> 1980's I believe. The term Multi dates back to Sept. 20, 2009. Here is
> the first post to use the word in this context.
>
> http://www.twistypuzzles.com/forum/viewtopic.php?p=3D179035#p179035
>
> Before then the concept was know but it was also called Super so you had
> terminology like the Super-Super Cubes being used.
>
> Yes, you can buy the Circle 3x3x3 here:
> http://www.hknowstore.com/locale/en-US/item.aspx?corpname=3D
> nowstore&itemid=3D1e61975c-8343-4bce-81f9-54be14cf0cc2
>
> The Circle 4x4x4 is here: (not my auction)
> http://www.ebay.com/itm/252321959913
>
> The Double Circle Real 5x5x5 is here: (this is my Shapeways shop)
> http://shpws.me/CLly
>
>
>
> All of these are Super-Multi puzzles.
>
> Yes, there are other ways of breaking the degeneracies. You could put
> some 2D stickers on the faces of the 3D stickers for example. But I want=
ed
> to expose the core so the same approach could be used making a Super Mult=
i
> 4x4x4x4 etc. This is the most general approach that I know.
>
> Also, just a point of clarification, you say the center hypercubie can=E2=
=80=99t
> be scrambled anyway on the super multi 3x3x3x3, but this doesn=E2=80=99t =
mean the
> super multi 3x3x3x3 is the same to solve as the normal 3x3x3x3- the super
> multi version does break some degeneracies and increase the number of
> unsolved states of the puzzle, correct?
>
> It is the core hypercubie that can't be scrambled. All 8 cell center
> hypercubies can be scrambled, or at least their orientations can be as
> their positions never move. As to the second question, no that isn't wha=
t
> it means. It does mean however that the Super Multi 3x3x3x3 is the same
> solve as the Super 3x3x3x3. The Super 3x3x3x3 does have more states then
> the Normal 3x3x3x3. All Multi does for this puzzle is add the core. And
> you know the orientation of the core even if you cannot see it as all the
> cell centers are attached to it. For example a 3x3x3 has a hidden 27 cub=
ie
> we call the core on the inside. It is normally hidden out of view and
> unstickered but still you always know the red sticker on the core would b=
e
> directly below the red face center.
>
>
> Also note I'm just talking about the 3x3x3x3 here. The Super Multi
> 4x4x4x4 has more states then the Super 4x4x4x4 as it contains the 2x2x2x2
> on the inside.
>
>
> And I've been a member of MC4D since March 12, 2011. At least I have bee=
n
> getting the digest since then. I rarely have the time to read the digest
> and honestly I can not recall if I've ever posted before or not. So I
> certainly haven't been a very active member. The oldest post of mine I c=
an
> find on TwistyPuzzles.com
> 2004 and I was active in the forum in the form it had before it moved to
> the current site. I can remember making posts about Twisty Puzzles in
> various locations going back to the early to mid 1990's I believe. I
> remember requesting and being added to Jerry Slocum's Directory of Puzzle
> Collectors sometime in the 90's as well.
>
>
> I'm sad to say I'm not familiar with the origin of MC4D so I'm not certai=
n
> how long its been around.
>
>
> Carl
>
>
>
>
>=20
>
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ng it, I added some circle puzzles to MagicTile.=C2=A0 However, they don=
9;t match the behavior of the physical puzzles=C2=A0unless you artificially=
limit slicemask=C2=A0usage to only allow 2nd layer twists.=C2=A0 I added a=
circle cube and a circle Megaminx,=C2=A0but also a circle Klein quartic, w=
hich I thought justified this post.=C2=A0 When limited to 2nd layer twists,=
I think the circle KQ can represent a "super multi Klein quartic"=
;, and it's cool to think about a hidden 24-color genus-3 "cubie&q=
uot; :)
eens dave.reens@g=
mail.com [4D_Cubing] <yahoogroups.com" target=3D"_blank">4D_Cubing@yahoogroups.com>=
wrote:der-left:1px #ccc solid;padding-left:1ex">
=20=20=20=20=20=20=20=20
he great information and links. I'm definitely adding the 3x3x3 circle =
to my wish list, and maybe someday when I'm rich I'll have to buy y=
our 5x5x5 with the double circle :-), what an awesome creation.=C2=A0
On Jul 24, 2016, at 4:48 PM, <=
a href=3D"mailto:carl.n.hoff@gmail.com" target=3D"_blank">carl.n.hoff@gmail=
.com [4D_Cubing] <t=3D"_blank">4D_Cubing@yahoogroups.com> wrote:
=20
=20=20=20=20=20=20
=20=20=20=20=20=20
rd Super in this context has been around since the 1980's I believe.=C2=
=A0 The term Multi dates back to Sept. 20, 2009.=C2=A0 Here is the first po=
st to use the word in this context.
he concept was know but it was also called Super so you had terminology lik=
e the Super-Super Cubes being used.
uy the Circle 3x3x3 here:
4x4x4 is here: (not my auction)
5 is here: (this is my Shapeways shop)
=A0
e are other ways of breaking the degeneracies.=C2=A0 You could put some 2D =
stickers on the faces of the 3D stickers for example.=C2=A0 But I wanted to=
expose the core so the same approach could be used making a Super Multi 4x=
4x4x4 etc.=C2=A0 This is the most general approach that I know.
br>
ust a point of clarification, you say the center hypercubie can=E2=80=99t b=
e scrambled anyway on the super multi 3x3x3x3, but this doesn=E2=80=99t mea=
n the super multi 3x3x3x3 is the same to solve as the normal 3x3x3x3- the s=
uper multi version does break some degeneracies and increase the number of =
unsolved states of the puzzle, correct?
he core hypercubie that can't be scrambled.=C2=A0 All 8 cell center hyp=
ercubies can be scrambled, or at least their orientations can be as their p=
ositions never move.=C2=A0 As to the second question, no that isn't wha=
t it means.=C2=A0 It does mean however that the Super Multi 3x3x3x3 is the =
same solve as the Super 3x3x3x3.=C2=A0 The Super 3x3x3x3 does have more sta=
tes then the Normal 3x3x3x3.=C2=A0 All Multi does for this puzzle is add th=
e core.=C2=A0 And you know the orientation of the core even if you cannot s=
ee it as all the cell centers are attached to it.=C2=A0 For example a 3x3x3=
has a hidden 27 cubie we call the core on the inside.=C2=A0 It is normally=
hidden out of view and unstickered but still you always know the red stick=
er on the core would be directly below the red face center. =C2=A0
uper Multi 4x4x4x4 has more states then the Super 4x4x4x4 as it contains th=
e 2x2x2x2 on the inside.
D since March 12, 2011.=C2=A0 At least I have been getting the digest since=
then.=C2=A0 I rarely have the time to read the digest and honestly I can n=
ot recall if I've ever posted before or not.=C2=A0 So I certainly haven=
't been a very active member.=C2=A0 The oldest post of mine I can find =
on TwistyPuzzles.com=
is dated December 2, 2004 and I was active in the forum in the form it=
had before it moved to the current site.=C2=A0 I can remember making posts=
about Twisty Puzzles in various locations going back to the early to mid 1=
990's I believe.=C2=A0 I remember requesting and being added to=C2=A0Je=
rry Slocum's Directory of Puzzle Collectors sometime in the 90's as=
well.
igin of MC4D so I'm not certain how long its been around.
>
=20=20=20=20=20
=20=20=20=20
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