# 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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> Yahoo! Groups Links

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