Message #2802

From: Roice Nelson <roice3@gmail.com>
Subject: Re: [MC4D] RE: MagicTile {∞,3} solutions
Date: Sun, 10 Nov 2013 21:49:57 -0600

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

Thanks again Andrey!

Roice

On Tue, Oct 29, 2013 at 10:46 AM, Roice Nelson <roice3@gmail.com> 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
>
> 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
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>
>