8-demicubic honeycomb

8-demicubic honeycomb
(No image)
Type	Uniform 8-space honeycomb
Family	Alternated hypercube honeycomb
Schläfli symbol	h{4,3,3,3,3,3,3,4}
Coxeter-Dynkin diagram
Facets	{3,3,3,3,3,3,4} h{4,3,3,3,3,3,3}
Vertex figure	Rectified octacross
Coxeter group	${\tilde{B}}_8$ [4,3,3,3,3,3,31,1] ${\tilde{D}}_8$ [31,1,3,3,3,31,1]

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 facets. The 8-cubes become alternated into 8-demicubes h{4,3,3,3,3,3,3} and the alternated vertices create 8-orthoplex {3,3,3,3,3,3,4} facets .

Its vertex arrangement is called the D8 lattice.

Kissing number

This tessellation represents a dense sphere packing (With a Kissing number of 112, compared to the best possible of 240), with each vertex of this polytope represents the center point for one of the 112 7-spheres, and the central radius, equal to the edge length exactly fits one more 7-sphere.

See also

• Cubic honeycomb
• Alternated cubic honeycomb
• Demitesseractic honeycomb
• Demipenteractic honeycomb
• Demihexeractic honeycomb
• Demihepteractic honeycomb
• Uniform polytope

References

• Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8
  • pp. 154-156: Partial truncation or alternation, represented by h prefix: h{4,4}={4,4}; h{4,3,4}={3^1,1,4}, h{4,3,3,4}={3,3,4,3}, ...
• Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [1]
  • (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]

External links

• Olshevsky, George, Half measure polytope at Glossary for Hyperspace.