In
five-dimensional
A five-dimensional space is a space with five dimensions. In mathematics, a sequence of ''N'' numbers can represent a location in an ''N''-dimensional space. If interpreted physically, that is one more than the usual three spatial dimensions a ...
Euclidean geometry
Euclidean geometry is a mathematical system attributed to ancient Greek mathematics, Greek mathematician Euclid, which he described in his textbook on geometry: the ''Euclid's Elements, Elements''. Euclid's approach consists in assuming a small ...
, the quarter 5-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
A honeycomb is a mass of Triangular prismatic honeycomb#Hexagonal prismatic honeycomb, hexagonal prismatic Beeswax, wax cells built by honey bees in their beehive, nests to contain their larvae and stores of honey and pollen.
beekeeping, Beekee ...
). It has half the vertices of the
5-demicubic honeycomb, and a quarter of the vertices of a
5-cube honeycomb.
[Coxeter, Regular and Semi-Regular Polytopes III, (1988), p318] Its facets are
5-demicube
In five-dimensional geometry, a demipenteract or 5-demicube is a semiregular 5-polytope, constructed from a ''5-hypercube'' (penteract) with alternated vertices removed.
It was discovered by Thorold Gosset. Since it was the only semiregular 5- ...
s and
runcinated 5-demicube
In five-dimensional geometry, a steric 5-cube or (steric 5-demicube or sterihalf 5-cube) is a convex uniform 5-polytope. There are unique 4 steric forms of the 5-cube. Steric 5-cubes have half the vertices of stericated 5-cubes.
Steric 5-cube ...
s.
Related honeycombs
See also
Regular and uniform honeycombs in 5-space:
*
5-cube honeycomb
*
5-demicube honeycomb
*
5-simplex honeycomb
In Five-dimensional space, five-dimensional Euclidean geometry, the 5-simplex honeycomb or hexateric honeycomb is a space-filling tessellation (or honeycomb (geometry), honeycomb or pentacomb). Each vertex is shared by 12 5-simplexes, 30 rectified ...
*
Truncated 5-simplex honeycomb
*
Omnitruncated 5-simplex honeycomb
In Five-dimensional space, five-dimensional Euclidean geometry, the omnitruncated 5-simplex honeycomb or omnitruncated hexateric honeycomb is a space-filling tessellation (or honeycomb (geometry), honeycomb). It is composed entirely of omnitruncat ...
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
* x3o3o x3o3o *b3*e - spaquinoh
{{Honeycombs
Honeycombs (geometry)
6-polytopes