Message #2202

From: schuma <mananself@gmail.com>
Subject: Re: Making a puzzle based on 11-cell
Date: Sun, 27 May 2012 22:55:01 -0000

Hi Andrey,

I’m reading Coxeter’s paper "Ten toroids and fifty-seven hemi-dodecahedra", In section 5, he mentioned:

Grunbaum [1976, p. 197] went on to consider the possibility of using a non-orientable cell such as the hemi-dodecahedron {5, 3}/2 = {5, 3}5 or the hemi-icosahedron {3, 5}/2 = {3, 5}5. He found that 32 hemi-dodecahedra can be fitted together to make a polystroma of type {5, 3, 4}, and 11 hemi-icosahedra to make one of type {3, 5, 3}.

He’s referring to

Grunbaum, Branko: 1976, ‘Regularity of Graphs, Complexes and Designs’. Colloque CNRS, Problemes Combinatoires et Theorie des Graphes, Orsay.

I can’t find Grunbaum’s book/paper. But I wonder if the shape with 32 hemi-dodecahedra is what you’ve been looking for.

Nan

— In 4D_Cubing@yahoogroups.com, "Andrey" <andreyastrelin@…> wrote:
> It’s strange that there is no information about periodic patterns based on {4,3,5} or {5,3,4} - there should be some of them with not large number of colors…