Message #2801

From: Roice Nelson <roice3@gmail.com>
Subject: Re: [MC4D] RE: MagicTile {∞,3} solutions
Date: Tue, 29 Oct 2013 10:46:29 -0500

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

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@yahoo.com> 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
>
>
> As for EndRotation: look at this picture:
> 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, <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@…> 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@… 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
>
>
> Andrey
>
>
> —In 4d_cubing@yahoogroups.com, <roice3@…> <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
>
> 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@…> wrote:
>
>
>
> Roice,
>
> can you help me with this example:
> 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, <roice3@…> <roice3@…> wrote:
>
> Here is the documentation page for configuring colorings (made for
> Eduard a while back):
>
> 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@…> 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@… 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, <melinda@…> <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@…> wrote:
>
>
>
> Roice,
>
> can you help me with this example:
> 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, <roice3@…> <roice3@…> wrote:
>
> Here is the documentation page for configuring colorings (made for
> Eduard a while back):
>
> 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@…> 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@… 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, <melinda@…> <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
>
>
>
>
>
>
>
>
>
>
>
>
>
>