In
six-dimensional Euclidean geometry, the quarter 6-cubic honeycomb is a uniform space-filling
tessellation
A tessellation or tiling is the covering of a surface, often a plane (mathematics), plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to high-dimensional ...
(or
honeycomb). It has half the vertices of the
6-demicubic honeycomb, and a quarter of the vertices of a
6-cube honeycomb.
[Coxeter, Regular and Semi-Regular Polytopes III, (1988), p318] Its facets are
6-demicube
In geometry, a 6-demicube or demihexteract is a uniform 6-polytope, constructed from a ''6-cube'' ( hexeract) with alternated vertices removed. It is part of a dimensionally infinite family of uniform polytopes called demihypercubes.
E. L. Elte i ...
s,
stericated 6-demicubes, and ×
duoprisms.
Related honeycombs
See also
Regular and uniform honeycombs in 5-space:
*
6-cube honeycomb
*
6-demicube honeycomb
*
6-simplex honeycomb
In six-dimensional Euclidean geometry, the 6-simplex honeycomb is a space-filling tessellation (or honeycomb). The tessellation fills space by 6-simplex, rectified 6-simplex, and birectified 6-simplex facets. These facet types occur in proportion ...
*
Truncated 6-simplex honeycomb
*
Omnitruncated 6-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)
7-polytopes