# Message #2443

From: schuma <mananself@gmail.com>

Subject: Re: I’m solving the 600-cell

Date: Tue, 30 Oct 2012 16:25:43 -0000

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

> >

>