Thread: "I'm solving the 600-cell"

Hi guys,

I forgot to mention the complication of "full version" vs "simplified versi=
on".=20

In older MPUlt, as Eduard said, there's the "full version" of 600-cell. Thi=
s is announced by Audrey in this post in May 2011:

http://games.groups.yahoo.com/group/4D_Cubing/message/1745

It has 433 stickers in each cell. The total number of stickers is 259800. I=
t's a huge puzzle. It took my computer a few seconds to react when I drag t=
he view. I wasn't solving this one. But this is what a shallow-cut cell-tur=
ning 600-cell should look like. If you make the 600 cuts, then they really =
cut the puzzle into this many pieces.

In September 2011, Andrey announced a Simplified 600-cell, together with ma=
ny simplified 4D puzzles.

http://games.groups.yahoo.com/group/4D_Cubing/message/1874

In this simplified puzzle, many tiny pieces are discarded. Only the 1C cell=
centers, 2C face centers, 5C edges and 20C corners are kept. I think of it=
as more topologically correct than geometrically correct. It has 9000 stic=
kers, and around 2000 pieces that need to be solved. I was solving this one=
. By the way, both the simplified and full versions have 600 colors. In thi=
s sense they are all "full-color".

When Andrey added this puzzle, he dropped the full 600-cell. But there's a =
way to get the old monster back.

If you go to the directory of MPUlt and open MPUlt_puzzles.txt and search f=
or 600-cell, you'll find its definition. The fourth line says:=20

"Simplified"

That's the switch to simplified mode. Copy the definition of 600-cell, and =
paste it next to it. Change the name to full-600-cell, and remove the line =
"Simplified". Then you have a full 600-cell. You may also change the number=
s following "Cuts" to change the depth of cuts. For example, changing 0.968=
to 0.995 make the cuts more shallow.

~~~~~~~~~~~~
About solving the 600-cell

I solved all the pieces type by type. First face, then edges, then corners.=
The strategy of moving pieces is different from what I did for 120-cell.=20

For 120-cell, for each type of pieces, I have a 3-cycle algorithm, and I ch=
oose three particular pieces as the buffer pieces. I always find the destin=
ation, bring the destination to a buffer (setup), apply the 3-cycle, and se=
nd the destination back (undo setup).=20

For 600-cell. I use all the pieces on the surface of the spherical 3D view =
as buffer. The 3D view of 600-cell looks like a ball. All the cell on the s=
urface are geometrically very close to each other. So moving pieces between=
them is actually pretty fast. I have an algorithm to move a piece around t=
he surface. And I also have algorithms to directly send a surface piece to =
any layer deep into the ball. So every time I first find the destination of=
a surface piece, then move it on surface to the point directly on top of t=
he destination (like epicenter). Then send it towards the center to the cor=
rect layer. Then reorient it if necessary. I think this is an efficient str=
ategy for 600-cell. The last step of each type of pieces is to solve the wh=
ole surface.=20

The three cycles of all the types can be constructed by [1,1] commutator. J=
ust like 3x3x3x3, two face can be flipped simultaneously, and two edges als=
o. Unlike 3x3x3x3, the corner pieces can be rotated by itself to any direct=
ion. It's kind of convenient, otherwise orienting these 20C pieces would be=
a nightmare.

So, all the difficulty is in piece finding, and piece moving.=20

Nan

--- In 4D_Cubing@yahoogroups.com, "Eduard Baumann" wrote:
>
> Congratulations from me too!
>=20
> I didn't know that there is a newer version of MPUlt. I had only vers 1.0=
6 with the complete 600cell.
> The simplified 600cell is disponible in vers 1.08 (and the complete 600ce=
ll not anymore).
>=20
> Regards
> Ed
>=20
>=20
> ----- Original Message -----=20
> From: schuma=20
> To: 4D_Cubing@yahoogroups.com=20
> Sent: Tuesday, October 30, 2012 4:02 AM
> Subject: [MC4D] Re: I'm solving the 600-cell
>=20
>=20
>=20=20=20=20=20
> Solved! I just solved it, the cell-turning 600-cell. It took me 102312 =
moves, and 37 hours in nine days. The log file can be found here:
>=20
> http://games.groups.yahoo.com/group/4D_Cubing/files/Nan%20Ma/600_cell/6=
00cell_solved.zip
>=20
> and can be opened by MPUlt 1.08. After all it's not as painful as I exp=
ected ...
>=20
> So, all the six regular polytopes in 4D have been solved!
>=20
> Again this is only a simplified version instead of the full shallow cut=
600-cell, speaking of which, I can't imagine how to deal with it.
>=20
> Nan
>=20
> --- In 4D_Cubing@yahoogroups.com, "schuma" wrote:
> >
> > Hi guys,
> >=20
> > Since last weekend I've been solving the 600-cell using MPUlt. Of cou=
rse I'm solving the "simplified" version with about 2,000 pieces, but not t=
he full version with over 200,000 pieces.
> >=20
> > Now I've spent 21+ hours, and have solved all the 1200 2C face pieces=
. Then I need to deal with 720 5C edges, and 120 corner pieces. In terms of=
number of pieces it sounds easier than the 120-cell. But visually this puz=
zle is, I would say, more complicated. Because in the 120-cell, you basical=
ly see 120 things, whereas here you see 600 things. Because of this differe=
nce, I'm taking a different approach of moving the pieces around. This meth=
od is working well so far.
> >=20
> > I posted a screenshot here:
> >=20
> > http://games.groups.yahoo.com/group/4D_Cubing/files/Nan%20Ma/600_cell=
/Image%20000.png
> >=20
> > I hope in a several days or weeks I can solve the whole puzzle.=20
> >=20
> > Andrey, thanks again for making MPUlt!
> >=20
> > Nan
> >
>

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Hello Nan,

Thanks for the description of the puzzle and your solution approach. I
like your idea of solving the "nearest" (surface) parts first. The
analogy to 3D is to reorient the puzzle when you do not need to. Your
technique of sending pieces straight towards the middle (the far side)
is new to me and seems like a very clever idea. It reminds me of a
classic video game where you would move your ship (or whatever that
thing was) around the perimeter of a polygonal opening of a sort of tube
viewed edge on. Maybe some enemy ships would be climbing out of the tube
and your goal was to drop bombs down the side of the tube to hit them.
Unfortunately I can't remember the game's name but maybe someone else will.

I agree that the "simplified" 600-cell sounds like the best definition
of the proper puzzle. I agree that what you call the "topologically
correct" form is best. Geometrically defined cuts give a fine way to
begin to create a puzzle but I do not see a good reason to insist that
that always results the best puzzle description.

So what will you do next? Shall we ask Andrey to create an omnitruncated
600-cell

puzzle for you? :-)

Best,
-Melinda

On 10/30/2012 9:25 AM, schuma wrote:
> Hi guys,
>
> I forgot to mention the complication of "full version" vs "simplified version".
>
> In older MPUlt, as Eduard said, there's the "full version" of 600-cell. This is announced by Audrey in this post in May 2011:
>
> http://games.groups.yahoo.com/group/4D_Cubing/message/1745
>
> It has 433 stickers in each cell. The total number of stickers is 259800. It's a huge puzzle. It took my computer a few seconds to react when I drag the view. I wasn't solving this one. But this is what a shallow-cut cell-turning 600-cell should look like. If you make the 600 cuts, then they really cut the puzzle into this many pieces.
>
> In September 2011, Andrey announced a Simplified 600-cell, together with many simplified 4D puzzles.
>
> http://games.groups.yahoo.com/group/4D_Cubing/message/1874
>
> In this simplified puzzle, many tiny pieces are discarded. Only the 1C cell centers, 2C face centers, 5C edges and 20C corners are kept. I think of it as more topologically correct than geometrically correct. It has 9000 stickers, and around 2000 pieces that need to be solved. I was solving this one. By the way, both the simplified and full versions have 600 colors. In this sense they are all "full-color".
>
> When Andrey added this puzzle, he dropped the full 600-cell. But there's a way to get the old monster back.
>
> If you go to the directory of MPUlt and open MPUlt_puzzles.txt and search for 600-cell, you'll find its definition. The fourth line says:
>
> "Simplified"
>
> That's the switch to simplified mode. Copy the definition of 600-cell, and paste it next to it. Change the name to full-600-cell, and remove the line "Simplified". Then you have a full 600-cell. You may also change the numbers following "Cuts" to change the depth of cuts. For example, changing 0.968 to 0.995 make the cuts more shallow.
>
> ~~~~~~~~~~~~
> About solving the 600-cell
>
> I solved all the pieces type by type. First face, then edges, then corners. The strategy of moving pieces is different from what I did for 120-cell.
>
> For 120-cell, for each type of pieces, I have a 3-cycle algorithm, and I choose three particular pieces as the buffer pieces. I always find the destination, bring the destination to a buffer (setup), apply the 3-cycle, and send the destination back (undo setup).
>
> For 600-cell. I use all the pieces on the surface of the spherical 3D view as buffer. The 3D view of 600-cell looks like a ball. All the cell on the surface are geometrically very close to each other. So moving pieces between them is actually pretty fast. I have an algorithm to move a piece around the surface. And I also have algorithms to directly send a surface piece to any layer deep into the ball. So every time I first find the destination of a surface piece, then move it on surface to the point directly on top of the destination (like epicenter). Then send it towards the center to the correct layer. Then reorient it if necessary. I think this is an efficient strategy for 600-cell. The last step of each type of pieces is to solve the whole surface.
>
> The three cycles of all the types can be constructed by [1,1] commutator. Just like 3x3x3x3, two face can be flipped simultaneously, and two edges also. Unlike 3x3x3x3, the corner pieces can be rotated by itself to any direction. It's kind of convenient, otherwise orienting these 20C pieces would be a nightmare.
>
> So, all the difficulty is in piece finding, and piece moving.
>
> Nan
>
> --- In 4D_Cubing@yahoogroups.com, "Eduard Baumann" wrote:
>> Congratulations from me too!
>>
>> I didn't know that there is a newer version of MPUlt. I had only vers 1.06 with the complete 600cell.
>> The simplified 600cell is disponible in vers 1.08 (and the complete 600cell not anymore).
>>
>> Regards
>> Ed
>>
>>
>> ----- Original Message -----
>> From: schuma
>> To: 4D_Cubing@yahoogroups.com
>> Sent: Tuesday, October 30, 2012 4:02 AM
>> Subject: [MC4D] Re: I'm solving the 600-cell
>>
>>
>>
>> Solved! I just solved it, the cell-turning 600-cell. It took me 102312 moves, and 37 hours in nine days. The log file can be found here:
>>
>> http://games.groups.yahoo.com/group/4D_Cubing/files/Nan%20Ma/600_cell/600cell_solved.zip
>>
>> and can be opened by MPUlt 1.08. After all it's not as painful as I expected ...
>>
>> So, all the six regular polytopes in 4D have been solved!
>>
>> Again this is only a simplified version instead of the full shallow cut 600-cell, speaking of which, I can't imagine how to deal with it.
>>
>> Nan
>>
>> --- In 4D_Cubing@yahoogroups.com, "schuma" wrote:
>> >
>> > Hi guys,
>> >
>> > Since last weekend I've been solving the 600-cell using MPUlt. Of course I'm solving the "simplified" version with about 2,000 pieces, but not the full version with over 200,000 pieces.
>> >
>> > Now I've spent 21+ hours, and have solved all the 1200 2C face pieces. Then I need to deal with 720 5C edges, and 120 corner pieces. In terms of number of pieces it sounds easier than the 120-cell. But visually this puzzle is, I would say, more complicated. Because in the 120-cell, you basically see 120 things, whereas here you see 600 things. Because of this difference, I'm taking a different approach of moving the pieces around. This method is working well so far.
>> >
>> > I posted a screenshot here:
>> >
>> > http://games.groups.yahoo.com/group/4D_Cubing/files/Nan%20Ma/600_cell/Image%20000.png
>> >
>> > I hope in a several days or weeks I can solve the whole puzzle.
>> >
>> > Andrey, thanks again for making MPUlt!
>> >
>> > Nan
>> >
>>
>
>
> ------------------------------------
>
> Yahoo! Groups Links
>
>
>
>


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Hello Nan,



Thanks for the description of the puzzle and your solution approach.
I like your idea of solving the "nearest" (surface) parts first. The
analogy to 3D is to reorient the puzzle when you do not need to.
Your technique of sending pieces straight towards the middle (the
far side) is new to me and seems like a very clever idea. It reminds
me of a classic video game where you would move your ship (or
whatever that thing was) around the perimeter of a polygonal opening
of a sort of tube viewed edge on. Maybe some enemy ships would be
climbing out of the tube and your goal was to drop bombs down the
side of the tube to hit them. Unfortunately I can't remember the
game's name but maybe someone else will.



I agree that the "simplified" 600-cell sounds like the best
definition of the proper puzzle. I agree that what you call the
"topologically correct" form is best. Geometrically defined cuts
give a fine way to begin to create a puzzle but I do not see a good
reason to insist that that always results the best puzzle
description.



So what will you do next? Shall we ask Andrey to create an href="http://en.wikipedia.org/wiki/Omnitruncated_120-cell#Omnitruncated_600-cell">omnitruncated
600-cell puzzle for you?  :-)



Best,

-Melinda

Hi guys,

I forgot to mention the complication of "full version" vs "simplified version". 

In older MPUlt, as Eduard said, there's the "full version" of 600-cell. This is announced by Audrey in this post in May 2011:

http://games.groups.yahoo.com/group/4D_Cubing/message/1745

It has 433 stickers in each cell. The total number of stickers is 259800. It's a huge puzzle. It took my computer a few seconds to react when I drag the view. I wasn't solving this one. But this is what a shallow-cut cell-turning 600-cell should look like. If you make the 600 cuts, then they really cut the puzzle into this many pieces.

In September 2011, Andrey announced a Simplified 600-cell, together with many simplified 4D puzzles.

http://games.groups.yahoo.com/group/4D_Cubing/message/1874

In this simplified puzzle, many tiny pieces are discarded. Only the 1C cell centers, 2C face centers, 5C edges and 20C corners are kept. I think of it as more topologically correct than geometrically correct. It has 9000 stickers, and around 2000 pieces that need to be solved. I was solving this one. By the way, both the simplified and full versions have 600 colors. In this sense they are all "full-color".

When Andrey added this puzzle, he dropped the full 600-cell. But there's a way to get the old monster back.

If you go to the directory of MPUlt and open MPUlt_puzzles.txt and search for 600-cell, you'll find its definition. The fourth line says: 

"Simplified"

That's the switch to simplified mode. Copy the definition of 600-cell, and paste it next to it. Change the name to full-600-cell, and remove the line "Simplified". Then you have a full 600-cell. You may also change the numbers following "Cuts" to change the depth of cuts. For example, changing 0.968 to 0.995 make the cuts more shallow.

~~~~~~~~~~~~
About solving the 600-cell

I solved all the pieces type by type. First face, then edges, then corners. The strategy of moving pieces is different from what I did for 120-cell. 

For 120-cell, for each type of pieces, I have a 3-cycle algorithm, and I choose three particular pieces as the buffer pieces. I always find the destination, bring the destination to a buffer (setup), apply the 3-cycle, and send the destination back (undo setup). 

For 600-cell. I use all the pieces on the surface of the spherical 3D view as buffer. The 3D view of 600-cell looks like a ball. All the cell on the surface are geometrically very close to each other. So moving pieces between them is actually pretty fast. I have an algorithm to move a piece around the surface. And I also have algorithms to directly send a surface piece to any layer deep into the ball. So every time I first find the destination of a surface piece, then move it on surface to the point directly on top of the destination (like epicenter). Then send it towards the center to the correct layer. Then reorient it if necessary. I think this is an efficient strategy for 600-cell. The last step of each type of pieces is to solve the whole surface. 

The three cycles of all the types can be constructed by [1,1] commutator. Just like 3x3x3x3, two face can be flipped simultaneously, and two edges also. Unlike 3x3x3x3, the corner pieces can be rotated by itself to any direction. It's kind of convenient, otherwise orienting these 20C pieces would be a nightmare.

So, all the difficulty is in piece finding, and piece moving. 

Nan

--- In 4D_Cubing@yahoogroups.com, "Eduard Baumann" <baumann@...> wrote:

Congratulations from me too!

I didn't know that there is a newer version of MPUlt. I had only vers 1.06 with the complete 600cell.
The simplified 600cell is disponible in vers 1.08 (and the complete 600cell not anymore).

Regards
Ed


  ----- Original Message ----- 
  From: schuma 
  To: 4D_Cubing@yahoogroups.com 
  Sent: Tuesday, October 30, 2012 4:02 AM
  Subject: [MC4D] Re: I'm solving the 600-cell


    
  Solved! I just solved it, the cell-turning 600-cell. It took me 102312 moves, and 37 hours in nine days. The log file can be found here:

  http://games.groups.yahoo.com/group/4D_Cubing/files/Nan%20Ma/600_cell/600cell_solved.zip

  and can be opened by MPUlt 1.08. After all it's not as painful as I expected ...

  So, all the six regular polytopes in 4D have been solved!

  Again this is only a simplified version instead of the full shallow cut 600-cell, speaking of which, I can't imagine how to deal with it.

  Nan

  --- In 4D_Cubing@yahoogroups.com, "schuma" <mananself@> wrote:
  >
  > Hi guys,
  > 
  > Since last weekend I've been solving the 600-cell using MPUlt. Of course I'm solving the "simplified" version with about 2,000 pieces, but not the full version with over 200,000 pieces.
  > 
  > Now I've spent 21+ hours, and have solved all the 1200 2C face pieces. Then I need to deal with 720 5C edges, and 120 corner pieces. In terms of number of pieces it sounds easier than the 120-cell. But visually this puzzle is, I would say, more complicated. Because in the 120-cell, you basically see 120 things, whereas here you see 600 things. Because of this difference, I'm taking a different approach of moving the pieces around. This method is working well so far.
  > 
  > I posted a screenshot here:
  > 
  > http://games.groups.yahoo.com/group/4D_Cubing/files/Nan%20Ma/600_cell/Image%20000.png
  > 
  > I hope in a several days or weeks I can solve the whole puzzle. 
  > 
  > Andrey, thanks again for making MPUlt!
  > 
  > Nan
  >

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

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--047d7b10ce611ad79304cd4d337b
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The video game is "Tempest". I recognized your description quickly because
we have a restored full-size version of this at my work :D

http://en.wikipedia.org/wiki/Tempest_(video_game)

I'd like to add my congrats to the chorus. Awesome job Nan! And awesome
job Ed for hitting the 200 mark in MagicTile! You guys are incredible.

Cheers,
Roice


On Tue, Oct 30, 2012 at 3:38 PM, Melinda Green wrote:

>
>
> Hello Nan,
>
> Thanks for the description of the puzzle and your solution approach. I
> like your idea of solving the "nearest" (surface) parts first. The analogy
> to 3D is to reorient the puzzle when you do not need to. Your technique of
> sending pieces straight towards the middle (the far side) is new to me and
> seems like a very clever idea. It reminds me of a classic video game where
> you would move your ship (or whatever that thing was) around the perimeter
> of a polygonal opening of a sort of tube viewed edge on. Maybe some enemy
> ships would be climbing out of the tube and your goal was to drop bombs
> down the side of the tube to hit them. Unfortunately I can't remember the
> game's name but maybe someone else will.
>
> I agree that the "simplified" 600-cell sounds like the best definition of
> the proper puzzle. I agree that what you call the "topologically correct"
> form is best. Geometrically defined cuts give a fine way to begin to create
> a puzzle but I do not see a good reason to insist that that always results
> the best puzzle description.
>
> So what will you do next? Shall we ask Andrey to create an omnitruncated
> 600-cellpuzzle for you? :-)
>
> Best,
> -Melinda
>
>

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The video game is "Tempest". =A0I recognized your description qui=
ckly because we have a restored full-size version of this at my work :D>

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That's it! I never liked that game too much but I was looking for the
title in case Nan might like to use it to name his method. My favorite
game was Battle Zone, followed by Asteroids. I very nearly had my own
restored Battle Zone but the restoration didn't work out. The graphics
were all wireframe models where the electron gun would stroke out
beautiful lines directly as opposed to raster displays with discrete
pixels. The immersive sound was awesome too. Later on, SGI implemented a
shaded, color, raster networked demo version based on a team-based
version of "capture the flag". When I worked at Autodesk, everyone who
had access to an SGI machine would log-in at 5 PM for epic battles.

-Melinda

On 10/30/2012 2:09 PM, Roice Nelson wrote:
>
>
> The video game is "Tempest". I recognized your description quickly
> because we have a restored full-size version of this at my work :D
>
> http://en.wikipedia.org/wiki/Tempest_(video_game)
>
>
> I'd like to add my congrats to the chorus. Awesome job Nan! And
> awesome job Ed for hitting the 200 mark in MagicTile! You guys are
> incredible.
>
> Cheers,
> Roice
>
>
> On Tue, Oct 30, 2012 at 3:38 PM, Melinda Green
> > wrote:
>
>
>
> Hello Nan,
>
> Thanks for the description of the puzzle and your solution
> approach. I like your idea of solving the "nearest" (surface)
> parts first. The analogy to 3D is to reorient the puzzle when you
> do not need to. Your technique of sending pieces straight towards
> the middle (the far side) is new to me and seems like a very
> clever idea. It reminds me of a classic video game where you would
> move your ship (or whatever that thing was) around the perimeter
> of a polygonal opening of a sort of tube viewed edge on. Maybe
> some enemy ships would be climbing out of the tube and your goal
> was to drop bombs down the side of the tube to hit them.
> Unfortunately I can't remember the game's name but maybe someone
> else will.
>
> I agree that the "simplified" 600-cell sounds like the best
> definition of the proper puzzle. I agree that what you call the
> "topologically correct" form is best. Geometrically defined cuts
> give a fine way to begin to create a puzzle but I do not see a
> good reason to insist that that always results the best puzzle
> description.
>
> So what will you do next? Shall we ask Andrey to create an
> omnitruncated 600-cell
>
> puzzle for you? :-)
>
> Best,
> -Melinda
>
>
>
>


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http-equiv="Content-Type">


That's it! I never liked that game too much but I was looking for
the title in case Nan might like to use it to name his method. My
favorite game was Battle Zone, followed by Asteroids. I very nearly
had my own restored Battle Zone but the restoration didn't work out.
The graphics were all wireframe models where the electron gun would
stroke out beautiful lines directly as opposed to raster displays
with discrete pixels. The immersive sound was awesome too. Later on,
SGI implemented a shaded, color, raster networked demo version based
on a team-based version of "capture the flag". When I worked at
Autodesk, everyone who had access to an SGI machine would log-in at
5 PM for epic battles.



-Melinda