In
seven-dimensional Euclidean geometry, the quarter 8-cubic honeycomb is a uniform space-filling
tessellation (or
honeycomb). It has half the vertices of the
8-demicubic honeycomb, and a quarter of the vertices of a
8-cube honeycomb.
[Coxeter, Regular and Semi-Regular Polytopes III, (1988), p318] Its facets are
8-demicubes h,
pentic 8-cube
In eight-dimensional geometry, an eight-dimensional polytope or 8-polytope is a polytope contained by 7-polytope facets. Each 6-polytope ridge being shared by exactly two 7-polytope facets.
A uniform 8-polytope is one which is vertex-transitive, ...
s h
6, × and ×
duoprisms.
See also
Regular and uniform honeycombs in 8-space:
*
8-cube honeycomb
*
8-demicube honeycomb
The 8-demicubic honeycomb, or demiocteractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 8-space. It is constructed as an alternation of the regular 8-cubic honeycomb.
It is composed of two different types of fa ...
*
8-simplex honeycomb
In eighth-dimensional Euclidean geometry, the 8-simplex honeycomb is a space-filling tessellation (or honeycomb). The tessellation fills space by 8-simplex, rectified 8-simplex, birectified 8-simplex, and trirectified 8-simplex facets. These fac ...
*
Truncated 8-simplex honeycomb
In Eighth dimension, eight-dimensional Euclidean geometry, the cyclotruncated 8-simplex honeycomb is a space-filling tessellation (or honeycomb (geometry), honeycomb). The tessellation fills space by 8-simplex, truncated 8-simplex, bitruncated 8-s ...
*
Omnitruncated 8-simplex honeycomb
Notes
References
* Kaleidoscopes: Selected Writings of
H. S. M. Coxeter
Harold Scott MacDonald "Donald" Coxeter, (9 February 1907 – 31 March 2003) was a British and later also Canadian geometer. He is regarded as one of the greatest geometers of the 20th century.
Biography
Coxeter was born in Kensington t ...
, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
** (Paper 24) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes III'',
ath. Zeit. 200 (1988) 3-45See p31
*
{{Honeycombs
Honeycombs (geometry)
9-polytopes