Message #2587

From: Roice Nelson <roice3@gmail.com>
Subject: Re: [MC4D] MagicTile Coloring
Date: Tue, 01 Jan 2013 15:47:32 -0600

Hi Ed,

Yep, I’ve been following your posts and progress. Nice job on all your
solves btw! Getting to the half-way mark would be a big milestone, and I
hope you make it.

I may be missing something, but it seems that if you recolor one of the
triangular prisms by cycling the 3 colors on it, the puzzle hasn’t really
changed. So it seems to me that all of the colorings you are describing
are equivalent. It is still a 30-faced puzzle with 30 colors, connected up
with the same global topology. The edge sets in this puzzle had to be made
to fit the topology of the {4,6|3} skew polyhedron, and changing the edge
sets would change the topology (resulting in some other shape).

But maybe you are thinking something else. Are you talking about twisting
up one of the triangular prisms and re-gluing, such that one triangle base
remains unchanged and the other is rotated 60 degrees? If so, that would
indeed be different, but the resulting shape wouldn’t be this skew
polyhedron, and MagicTile can’t currently support something like this.

Here’s some links I used when making these two puzzles. They might be
helpful for further study.

• For the {4,6|3}, the wikipedia page on the runcinated
  5-cell<http://en.wikipedia.org/wiki/Runcinated_5-cell#Runcinated_5-cell>
  .
  
• For the {6,4|3}, the wikipedia page on the bitruncated
  5-cell<http://en.wikipedia.org/wiki/Bitruncated_5-cell#Bitruncated_5-cell>
  .
  
• Also, see the section ‘Finite regular skew polyhedra of
  4-space<http://en.wikipedia.org/wiki/Regular_skew_polyhedron#Finite_regular_skew_polyhedra_of_4-space>‘
  for other topology possibilities (unfortunately, most would have too many
  faces to make good puzzles).

Let me know if I’m on track with my understanding.

seeya,
Roice

On Mon, Dec 31, 2012 at 1:03 PM, Eduard <ed.baumann@bluewin.ch> wrote:

> Hi Roice,
>
> Have you seen my description of the organisation of "MT skew {4,6|3} 30
> v020" ?
> Each 3-prismatique edge can be untwisted or twisted by +60° or -60°
> (separated from tetrahedron-vertex and reglued). So 10^3 different
> colorings can be constructed. That’s a lot. Are some of them equivalent?
> Is it difficult to find the corresponding "edge-sets"?
>
> Kind regards
> Ed
>
>
>
> ————————————
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