Message #2319

From: Andrey <andreyastrelin@yahoo.com>
Subject: [MC4D] Re: Hyperbolic Honeycomb {7,3,3}
Date: Fri, 06 Jul 2012 09:56:04 -0000

>
> Ah right, good. That’s the 2d face of it…
> Okay… and I was wondering if the same process could be used in 3d, to find
> your 3d convex object (I think you’re calling it {3*,3})
> directly, as a sub-structure of some more "ordinary" uniform honeycomb.
> But given the answer to 1), I think probably not.
>
If you allow different lengths of edges in the honeycomb (it will be vertex- and cell-transitive, but not exactly uniform) you can build it from truncated tetrahedra - 14 of them meets in every vertex and dual cell will be 7-prism (but I can’t imagine this dual honeycomb where 12 7-prisms meet in the vertex :) ) Then cell of {3*,3,7} will be union of some cells of that honeycomb.