Message #3455

From: Dave Reens <dave.reens@gmail.com>
Subject: Re: [MC4D] 3^4 solved
Date: Sat, 16 Jul 2016 08:07:58 -0600

Hi Roice,

Thanks for your clear answer, and for those links! Yeah I’m sure a ground up rewrite isn’t too appealing. I’m really impressed that icosidodecahedron and great rhombicosidodecahedron physical puzzles exist though, wouldn’t have guessed. It’s interesting how the slicing of the soccer ball puts pentagrams on the pentagon faces. Well I guess that’s obvious. In fact I guess you can slice a pentagram so as to get pentagons as well. Maybe there are Archimedean twisty puzzles that are the "duals" of uniform twisty puzzles in the sense that one puzzle can be thought of as a sliced version of either polyhedron?

That’s interesting about other transitivity violations for polytopes. It’s obvious that "face polyhedron" transitivity gets violated for a bunch of the prismatic ones. I’ll have to try to think about face and edge transitivity too though- seems like a fun mental challenge :-)

Dave

> On Jul 14, 2016, at 4:19 PM, Roice Nelson roice3@gmail.com [4D_Cubing] <4D_Cubing@yahoogroups.com> wrote:
>
> Hi Dave,
>
> Regarding your question about the archimedean/uniform polyhedra, that’s totally possible! I’ve seen some physical puzzles using archimedean solids, like here and here. I don’t know of software doing this, but would be surprised if some didn’t exist somewhere. Anybody here know any? (That was a slight lie, because one version of Don’s MC4D that hasn’t been released supports 3D archimedean variants.)
>
> Unfortunately MagicTile does not support this yet. It only supports surfaces whose universal cover is a regular tiling. There are some puzzles that are irregular in the sense of colorings rather than the underlying tiling, but that’s different than what you are asking about. I’d like it to support uniform tilings, but it would be a big undertaking and likely require a ground-up rewrite.
>
> I did want to point out that MC4D supports a lot of uniform polytopes (by which I mean the polytope is vertex-transitive, but not transitive on all flags - there are more ways a dimension up for things to be irregular, and the term "uniform" doesn’t really capture that).
>
> Best,
> Roice
>
>
>> On Tue, Jul 12, 2016 at 11:06 PM, David Reens dave.reens@gmail.com [4D_Cubing] <4D_Cubing@yahoogroups.com> wrote:
>>
>>
>> Ah Thanks Ray. I had gotten as far as zhumala with MC7D- wanting to try higher dim cubes but not understanding what clicking was doing and not finding directions in the ten minutes I devoted to the project. It looks like everything I might want is in that link.
>>
>> By the way is it possible to make twisty puzzles out of the Archimedian solids in 3D and not just platonic? How about uniform polyhedra? Could I do any of this in MagicTile? I haven’t tried it out yet.
>>
>> Cheers,
>> Dave
>>
>>> On Jul 12, 2016, at 5:28 PM, Ray Zhao thermostatico@gmail.com [4D_Cubing] <4D_Cubing@yahoogroups.com> wrote:
>>>
>>>
>>> Hi there,
>>>
>>> Tagging things sounds real awesome. I’ve no idea how it works though – is there a range limit?
>>>
>>> Great job with the 3^4, and even better (in my super-biased opinion) that you want to go solve even more higher-dimensional puzzles.
>>> I’ll post this just in case you haven’t seen it: http://astr73.narod.ru/MC7D/instr.html
>>> 3-click mode may be your thing.
>>>
>>> Also, do give MC5D a try, just in case it works out. I will admit however that it feels slightly buggier in some cases, especially on the 3^5.
>
>