Message #2805

From: andreyastrelin@yahoo.com
Subject: RE: MagicTile {∞,3} solutions
Date: Tue, 12 Nov 2013 11:11:34 -0800

Roice,
Here is my version of {12,4} 40 colors: https://www.dropbox.com/s/gmums460yu713q5/%7B12%2C4%7D%2040C.zip https://www.dropbox.com/s/gmums460yu713q5/%7B12%2C4%7D%2040C.zip . Actually, it’s just a combination of 8C (octahedron) and 5C (asymmetric {4,4} carpet). So combined puzzle should be asymmetric, and that’s why I don’t use Mirrored Edge Set.
My estimation is that I’ve added about a half of possible 4-reflection identities. What I don’t understand is why I don’t see white colors in some cells where it should be mapped by these reflections (like 3:3:3) - most of them are just black. I’ve tried to raise number of tiles up to 20000, but it doesn’t help.

The only non-trivial coloring of {12,3} is 24 colors - combination of cube and tetrahedron. Others are just versions of well-known spherical (or hemispherical) puzzles :)

Andrey

—In 4d_cubing@yahoogroups.com, <roice3@…> wrote:

Sweet, thank you! I will work on getting slicings setup for these and adding them (hopefully this weekend). We’ll probably have over 750 puzzles after this set, making Ed’s life more difficult if he wants to stay at the mark of solving half of all MagicTile puzzles :)

Any of the colorings you particularly like? Or any unusual ones?

On the {12,4} 40C, can you try upping NumTiles to a much higher value and see if it helps? (for example, even 15000 or more) Since the dodecagons are pretty large and there are many colors, the fundamental region will be big. My guess is that some of the identifications are long enough that they go beyond the initially generated tiling. That’s just a guess, but it is a problem I’ve encountered in the past. MagicTile will only recurse to a certain level regardless, and so this one may still not be possible. If you’d like to send me your working file, I can experiment with it some too.

Cheers,
Roice

On Mon, Nov 11, 2013 at 10:47 PM, <andreyastrelin@… mailto:andreyastrelin@…> wrote:

You are welcome :)
I’ve spent some time to design {12,4}, 40 colors pattern, but without success - even after entering of several dozens identities program doesn’t understand what do I want from it. So there are some simple {12,4} (4,5,6,8,9 colors) and some {12,3} (4,6,24 colors) patterns:
https://www.dropbox.com/s/x8t3g1u96zp12it/%7B12%2C3%7D%20.zip https://www.dropbox.com/s/x8t3g1u96zp12it/%7B12%2C3%7D%20.zip
https://www.dropbox.com/s/952748kam5fhjn9/%7B12%2C4%7D%20.zip https://www.dropbox.com/s/952748kam5fhjn9/%7B12%2C4%7D%20.zip
May be, I’ll be more lucky with {15,3}, 48 colors…

Andrey

—In 4d_cubing@yahoogroups.com mailto:4d_cubing@yahoogroups.com, <roice3@…> wrote:

The MagicTile download now has puzzles using Andrey’s {10,3} colorings. With about a dozen slicings configured for each coloring, there are 672 puzzles now (616 before).

www.gravitation3d.com/magictile/downloads/MagicTile_v2.zip http://www.gravitation3d.com/magictile/downloads/MagicTile_v2.zip

Thanks again Andrey!

Roice

On Tue, Oct 29, 2013 at 10:46 AM, Roice Nelson <roice3@… mailto:roice3@…> wrote:

Sweet, thanks for the 36C! I will add that one to the MT distribution as well. (Please feel free to keep them coming if you find more :D)

You are right that EndRotation does return us back to the white-green edge, and I edited your picture to help clarify what MagicTile is doing.

http://groups.yahoo.com/neo/groups/4D_Cubing/photos/albums/622194858/lightbox/2117008453 http://groups.yahoo.com/neo/groups/4D_Cubing/photos/albums/622194858/lightbox/2117008453

No rotations happen until the one at the very end. It is only performing reflections across the edges until then. So the portion on the white tile near A gets reflected to B, then C, then D. And from D, we just need one integer turn CCW to get to the final position, which is why EndRotation is 1. (By the way, the reflection edge indices and the EndRotation are always interpreted in a CCW sense on the tiling, regardless of whether we are on a mirrored face or not.)

It could have been better to implement it the way you thought it was working, because it can be difficult to figure out what EndRotation is needed. It’s hard to track what orientation the white tile is in after a set of reflections. I’ve often played "guess and check" with EndRotation, which has served me well at times because it produced unexpected colorings I would have never considered possible.

seeya,
Roice

On Tue, Oct 29, 2013 at 7:09 AM, <andreyastrelin@… mailto:andreyastrelin@…> wrote:

Roice,

{10,3} 18C is non-oriented! So it has 36-color twin: https://www.dropbox.com/s/8ed8wm202e9t7d4/%7B10%2C3%7D%2036C.xml https://www.dropbox.com/s/8ed8wm202e9t7d4/%7B10%2C3%7D%2036C.xml

As for EndRotation: look at this picture: https://www.dropbox.com/s/zyjhd5o88na810t/Screenshot%202013-10-28%2011.51.54.png https://www.dropbox.com/s/zyjhd5o88na810t/Screenshot%202013-10-28%2011.51.54.png
We start from white face, go to green, make 2 turns CCW, go to yellow, make 3 turns CCW, return to white. What should we do next? I thought that EndRotation should return us back to white-green edge (where we started - in this case it should be 2. Or may be 8, because we are on the mirrored face - but not 1), but it looks that it does something else. What does its value mean in this case?

Andrey

—In 4d_cubing@yahoogroups.com mailto:4d_cubing@yahoogroups.com, <roice3@…> wrote:

Yes, thanks Andrey! I will add these to the standard MagicTile distribution in the next few days. I’m going to configure some additional slicings on them first so we can have a bunch of puzzles to play on these new colorings (luckily, those are much easier to setup than finding working colorings).

I didn’t follow your question "So starting edge for "EndRotation" is unpredictable?". The EndRotation is applied to the tile after all the reflections have been done, and it affects all edges equally. The number here doesn’t signify an edge index. It specifies a rotation angle (the entered value multiplied by 2π/p). If this doesn’t clarify, can you describe more what you are asking?

Cheers,
Roice

On Mon, Oct 28, 2013 at 8:03 PM, Melinda Green <melinda@… mailto:melinda@…> wrote:

Great work, Andrey!
It looks to me like your 18-color puzzle is non-orientable (not "non-oriented") just like your 6-color puzzle. Readers should be aware that it’s extremely easy to add puzzles like these into MT. Just drop the XML files into the "MagicTile\config\user" folder.
-Melinda

On 10/28/2013 4:14 PM, andreyastrelin@… mailto:andreyastrelin@… wrote:

Hi Roice,
Thank you, now it makes sense. So starting edge for "EndRotation" is unpredictable?
I made four puzzles based on {10,3}. Three of them are copies of spherical and hemispherical puzzles and one (18 colors) looks like new one. Configuration files are here: https://www.dropbox.com/s/j32xshxy0nefk46/%7B10%2C3%7D.zip https://www.dropbox.com/s/j32xshxy0nefk46/%7B10%2C3%7D.zip

Andrey

—In 4d_cubing@yahoogroups.com mailto:4d_cubing@yahoogroups.com, <roice3@…> mailto:roice3@… wrote:

Hi Andrey,

Sorry for the delay. I was camping this weekend and disconnected from the interwebs.

To find working values, I looked at your file and compared your coloring configuration to the one for the hemidodecahedron. Two tags needed to be changed: "UseMirroredEdgeSet" needed to be set to false. That is true by default, but I’ve noticed it generally must be false for non-orientable puzzles. The hemidodec also had "EndRotation" = 1. Here is a working file, which only differs from your file by those two tags:

http://www.gravitation3d.com/magictile/4d_cubing/%7B10,3%7D%206C%20edited.xml http://www.gravitation3d.com/magictile/4d_cubing/%7B10,3%7D%206C%20edited.xml

I wanted to note that there was one required alteration to the hemidodecahedron coloring config. The elliptic puzzle had "InitialEdgeSet" = 1, but for the hyperbolic puzzle, this needed be left as the default (initial reflections across all edges) so it could fill out the whole plane. It is so interesting how the spherical puzzles can be expanded to hyperbolic tilings.

Hope this helps!

Roice

On Sat, Oct 26, 2013 at 12:41 PM, <andreyastrelin@… mailto:andreyastrelin@…> wrote:

Roice,
can you help me with this example: https://www.dropbox.com/s/bkb1runsvpyzooh/%7B10%2C3%7D%206C.xml https://www.dropbox.com/s/bkb1runsvpyzooh/%7B10%2C3%7D%206C.xml ?
It gives correct pattern of white faces, but keeps saying that all other tiles have the same color. But there should be 6 different colors (it’s hemidodecahedron expanded to {10,3}). I tried different values of EndRotation, but they don’t help. What do I do wrong?
Andrey

—In 4d_cubing@yahoogroups.com mailto:4d_cubing@yahoogroups.com, <roice3@…> mailto:roice3@… wrote:

Here is the documentation page for configuring colorings (made for Eduard a while back):

http://www.gravitation3d.com/magictile/info/identifications.html http://www.gravitation3d.com/magictile/info/identifications.html

I’ll be the first to admit that creating new colorings is not the easiest thing. I’m happy to answer questions though, or to discuss how it might be improved.

Cheers,
Roice

On Oct 24, 2013, at 11:39 PM, Melinda Green <melinda@… mailto:melinda@…> wrote:

OK, good to know, thanks Andrey. It surprises me a bit that puzzles with more colors are harder. That seems counter to the pattern where for example, the Rubik’s cube with 6 colors seems harder than the Megaminx with 12. Hopefully Roice will jump in with additional documentation on his puzzle file format. I would like to see what sort of fascinating new puzzles you come up with.

-Melinda

On 10/24/2013 4:46 PM, andreyastrelin@… mailto:andreyastrelin@… wrote:
Melinda, I’ve solved some of puzzles a couple of months ago, but there was nothing new for me - just versions of tetrahedron and cube. For something new we should try new coloring (with 12,24,36 colors etc.). Unfortunately I don’t understand Roice’s notation of puzzle definition, and can’t add good puzzles to MT.
Andrey

—In 4d_cubing@yahoogroups.com mailto:4d_cubing@yahoogroups.com, <melinda@…> mailto:melinda@… wrote:

Dear Cubists,

It’s been a while now since Roice added several (approximately) infinite
polygons to Magic Tile under "Hyperbolic > Large Polygons", and I’ve not
seen or heard of any solutions to the ones with more than three colors.
Has anyone done that? Even with 5 random twists I find myself hopelessly
lost, but then I’m not a strong solver. These new puzzles sure look
fabulous. How do they compare to the rest?

-Melinda

On Sat, Oct 26, 2013 at 12:41 PM, <andreyastrelin@… mailto:andreyastrelin@…> wrote:

—In 4d_cubing@yahoogroups.com mailto:4d_cubing@yahoogroups.com, <roice3@…> mailto:roice3@… wrote:

Here is the documentation page for configuring colorings (made for Eduard a while back):

http://www.gravitation3d.com/magictile/info/identifications.html http://www.gravitation3d.com/magictile/info/identifications.html

I’ll be the first to admit that creating new colorings is not the easiest thing. I’m happy to answer questions though, or to discuss how it might be improved.

Cheers,
Roice

On Oct 24, 2013, at 11:39 PM, Melinda Green <melinda@… mailto:melinda@…> wrote:

-Melinda

—In 4d_cubing@yahoogroups.com mailto:4d_cubing@yahoogroups.com, <melinda@…> mailto:melinda@… wrote:

Dear Cubists,

-Melinda