8-cubic honeycomb

8-cubic honeycomb
(no image)
Type	Regular 8-dimensional honeycomb
Family	Hypercube honeycomb
Schläfli symbol	{4,36,4} {4,35,31,1} t0,8{4,36,4} {∞}8
Coxeter-Dynkin diagrams
8-face type	{4,36}
7-face type	{4,35}
6-face type	{4,34}
5-face type	{4,33}
4-face type	{4,32}
Cell type	{4,3}
Face type	{4}
Face figure	{4,3} (octahedron)
Edge figure	8 {4,3,3} (16-cell)
Vertex figure	256 {4,36} (8-orthoplex)
Coxeter group	[4,36,4]
Dual	self-dual
Properties	vertex-transitive, edge-transitive, face-transitive, cell-transitive

The 8-cubic honeycomb or octeractic honeycomb is the only regular space-filling tessellation (or honeycomb) in Euclidean 8-space.

It is analogous to the square tiling of the plane and to the cubic honeycomb of 3-space, and the tesseractic honeycomb of 4-space.

There are many different Wythoff constructions of this honeycomb. The most symmetric form is regular, with Schläfli symbol {4,3⁶,4}. Another form has two alternating hypercube facets (like a checkerboard) with Schläfli symbol {4,3⁵,3^1,1}. The lowest symmetry Wythoff construction has 256 types of facets around each vertex and a prismatic product Schläfli symbol {∞}⁸.

See also

• Tesseractic honeycomb
• Penteractic honeycomb
• Hexeractic honeycomb
• Hepteractic honeycomb
• List of regular polytopes

References

• Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8 p.296, Table II: Regular honeycombs
• 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]

This geometry-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Geometry stubs Honeycombs (geometry) 9-polytopes Wikimedia Foundation. 2010. Игры ⚽ Нужна курсовая? 8-cube Hellenistic-era warships Look at other dictionaries: Cubic honeycomb — Type Regular honeycomb Family Hypercube honeycomb Schläfli symbol {4,3,4} Coxeter Dynkin diagram …   Wikipedia Bitruncated cubic honeycomb — The bitruncated cubic honeycomb is a space filling tessellation (or honeycomb) in Euclidean 3 space made up of truncated octahedra.It is one of 28 uniform honeycombs. It has 4 truncated octahedra around each vertex.It can be realized as the… …   Wikipedia Omnitruncated cubic honeycomb — Type Uniform honeycomb Schläfli symbol t0,1,2,3{4,3,4} Coxeter Dynkin diagram …   Wikipedia Quarter cubic honeycomb — The quarter cubic honeycomb is a space filling tessellation (or honeycomb) in Euclidean 3 space. It is composed of tetrahedra and truncated tetrahedra in a ratio of 1:1.It is vertex transitive with 6 truncated tetrahedra and 2 tetrahedra around… …   Wikipedia Cantitruncated cubic honeycomb — The cantitruncated cubic honeycomb is a uniform space filling tessellation (or honeycomb) in Euclidean 3 space, made up of truncated cuboctahedra, truncated octahedra, and cubes in a ratio of 1:1:3. Uniform colorings Cells can be shown in two… …   Wikipedia Truncated cubic honeycomb — The truncated cubic honeycomb is a uniform space filling tessellation (or honeycomb) in Euclidean 3 space. It is comprised of truncated cubes and octahedra in a ratio of 1:1. Symmetry There is a second uniform colorings by reflectional symmetry… …   Wikipedia Cantellated cubic honeycomb — The cantellated cubic honeycomb is a uniform space filling tessellation (or honeycomb) in Euclidean 3 space. It is comprised of small rhombicuboctahedra, cuboctahedra, and cubes in a ratio of 1:1:3 …   Wikipedia Runcitruncated cubic honeycomb — The runcitruncated cubic honeycomb is a uniform space filling tessellation (or honeycomb) in Euclidean 3 space. It is comprised of small rhombicuboctahedra, truncated cubes, octagonal prisms, and cubes in a ratio of 1:1:3:3 …   Wikipedia Order-5 cubic honeycomb — Poincaré disk models Type Hyperbolic regular honeycomb Schläfli symbol …   Wikipedia Gyroelongated alternated cubic honeycomb — The gyroelongated alternated cubic honeycomb is a space filling tessellation (or honeycomb) in Euclidean 3 space. It is composed of octahedra, triangular prisms, and tetrahedra in a ratio of 1:2:2.It is vertex uniform with 3 octahedra, 4… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”