Thread: "Omnitrucated simplex solved."

Hi all,
I just finished solve of the omnitruncated simplex. This object has 10 tr=
uncated 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:=20
At first, it has double group of simplex symmetry (like bitruncated simpl=
ex). 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 an=
d 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 an=
d 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 whol=
e 4D space by copies of it, and honeycomb vertex will have simplex structur=
e. So, there may be a set of finite periodic patterns and twisting puzzles =
based on it :)=20

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On Mon, Nov 21, 2011 at 12:07 AM, Andrey wrote:

> 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:
>

Nice :D

The fact that the size of some of these polytopes scare me away from
putting the effort into solutions, combined with your comment about solving
the 2C pieces manually made me think of a feature that might be nice for
our programs. I'm thinking of a way to control which type of pieces are
even a part of the puzzle. A 2C-only 3^4 for instance would be a simple
and enjoyable puzzle in and of itself, and one you could tackle in a few
minutes. The MPUlt "simplified" puzzles you made recently go this
direction, but maybe the control over which pieces are pruned could be
further extended.

> 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 :)
>

In looking at wiki about this honeycomb, I see the 8-cell, 16-cell, and
24-cell can also honeycomb 4D Euclidean space. When it comes to puzzles,
these are really more like 5D puzzles to us, being tessellations of 4D
cells. So very difficult! No one has solved any of the MS5D puzzles yet,
correct?

Roice

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