# Talk:24-cell honeycomb

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Mathematics rating:
 B Class
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Field: Geometry

## Unclear sections

A number of sections are written less than clearly.

For now: The section titled Symmetry constructions begins as follows:

"There are five different symmetry constructions of this tessellation. Each symmetry can be represented by different arrangements of colored 24-cell facets. In all cases, eight 24-cells meet at each vertex, but the vertex figures have different symmetry generators."

Sorry, but I do not understand what a "symmetry construction" is.

There is neither a definition nor a link.

Can we remove this section unless someone knowledgeable on the topic can define it so that at least a mathematician versed in geometry can understand it?

The 24-cell honeycomb can be defined from different ringed patterns of Coxeter diagrams. The geometry is the same in all constructions, but only the first one is regular, the rest uniform constructions. How would you propose this be improved? Tom Ruen (talk) 14:44, 12 March 2015 (UTC)

Also: Virtually all of the text in the section titled Related honeycombs is completely unclear about what exactly is its connection to the 24-cell honeycomb. (Yes, I do see that the same Coxeter group is mentioned. But maybe it can be explained just how that is relevant?)

Also: In the Related honeycombs section there are some numbers in parentheses: "(13)", "(19)", and "(24)". It is quite unclear what these numbers refer to. Can someone who knows please explain that in the article?Daqu (talk) 01:18, 12 March 2015 (UTC)

The related honeycombs is rather expansive, but useful for cross-referencing uniform honeycombs. The 24-cell honeycomb can be constructed from 4 different Coxeter groups, so each family is listed, with permutations of ringed patterns, each making a uniform honeycomb. The numbering are indexing from each family. The parenthesized indices express repeated honeycombs within the same family, so honeycomb 13 is the same as (13). Tom Ruen (talk) 14:44, 12 March 2015 (UTC)
Tom, whatever it means, my post is not so that someone will tell me the answer. The post is so that the article will become comprehensible.Daqu (talk) 13:07, 20 March 2015 (UTC)