# Message #1935

From: Andrey <andreyastrelin@yahoo.com>

Subject: Omnitrucated simplex solved.

Date: Mon, 21 Nov 2011 06:07:29 -0000

Hi all,

I just finished solve of the omnitruncated simplex. This object has 10 truncated octahedra cells, 20 hexagonal prism cells, simplex-like vertex, 150 2C pieces, 240 3Cs and 120 4Cs. So it’s not large for the modern standarts. But it is one of special uniform polychora:

At first, it has double group of simplex symmetry (like bitruncated simplex). For the puzzle it means that it has more families of stickers than we expect from it: 6 sets of 2C, 3 or 4 sets of 3C and 2 sets of 4C - and most of them needs different macros (but not 2C: I usually solve them manually - just to feel spirit of the puzzle :) )

Then, this polytope is alternable: you may remove half of its vertices and replace them by tetrahedra - and you’ll get vertex-transitive polychoron. Now I can’t imagine it (just know that it has 2 icosehadra, 2 octahedra and 6 irregular tetrhedra in each vertex). I don’t know, whether it is useful for puzzle making, but it will be good to look at it.

And, finally, there is omnitruncated simplex honeycomb! You can fill whole 4D space by copies of it, and honeycomb vertex will have simplex structure. So, there may be a set of finite periodic patterns and twisting puzzles based on it :)