Talk:5-simplex honeycomb

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)[reply]

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)[reply]

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)[reply]

Added. Tom Ruen (talk) 02:19, 22 November 2011 (UTC)[reply]