# Talk:5-simplex honeycomb

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Field: Geometry

## population

Each vertex is shared by 12 5-simplexes, 30 rectified 5-simplexes, and 20 birectified 5-simplexes.

So I'm guessing that the population of these cells in the tiling is in the ratio 2:2:1, respectively (i.e. 12/6 : 30/15 : 20/20). Right? Is that worth including? —Tamfang (talk) 21:04, 21 November 2011 (UTC)

These facets are easy to extract from the vertex figure, but I've not thought into how to compute ratios in the full tessellation. It would be good to have a summary from the whole family, under blank link simplectic honeycomb! I see the facet ratios in the 5-cell_honeycomb are given as 3:1, and Tetrahedral-octahedral_honeycomb is 2:1. There's also 6-simplex_honeycomb after this one.
Ah, Klitzing lists the tetracombs at [1], and [2], shows 1:1 ratio, so 5-cell_honeycomb is given wrong as 3:1. Tom Ruen (talk) 02:05, 22 November 2011 (UTC)
I see, looks like ratio is 1:1:1:1:1, with first/last are 5-simplex, second/penultimate are rect-5-simp, and middle is birect-5-simplex, so 2:2:1 is correct. Tom Ruen (talk) 02:11, 22 November 2011 (UTC)
Added. Tom Ruen (talk) 02:19, 22 November 2011 (UTC)