Omnitruncated cubic honeycomb

Omnitruncated cubic honeycomb
Type	Uniform honeycomb
Schläfli symbol	t0,1,2,3{4,3,4}
Coxeter-Dynkin diagram
Vertex figure	(tetrahedron)
Coxeter group	[4,3,4] [[4,3,4]] (doubled)
Dual	Dual omnitruncated cubic honeycomb
Properties	vertex-transitive

The omnitruncated cubic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 3-space. It is composed of truncated cuboctahedra and octagonal prisms in a ratio of 1:3.

A wireframe rendering

References

• George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
• Branko Grünbaum, Uniform tilings of 3-space. Geombinatorics 4(1994), 49 - 56.
• Norman Johnson Uniform Polytopes, Manuscript (1991)
• Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X. 
• Critchlow, Keith (1970). Order in Space: A design source book. Viking Press. ISBN 0-500-34033-1. 
• 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 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10] (1.9 Uniform space-fillings)
• A. Andreini, Sulle reti di poliedri regolari e semiregolari e sulle corrispondenti reti correlative (On the regular and semiregular nets of polyhedra and on the corresponding correlative nets), Mem. Società Italiana della Scienze, Ser.3, 14 (1905) 75–129.
• D. M. Y. Sommerville, An Introduction to the Geometry of n Dimensions. New York, E. P. Dutton, 1930. 196 pp. (Dover Publications edition, 1958) Chapter X: The Regular Polytopes
• Richard Klitzing, 3D Euclidean Honeycombs, x4x3x4x - otch - O20
• Uniform Honeycombs in 3-Space: 08-Otch

This Polychora article is a stub. You can help Wikipedia by expanding it.v · Categories: Polychora stubs Honeycombs (geometry) Wikimedia Foundation. 2010. Игры ⚽ Нужно сделать НИР? Snitch (song) Henry Hudson Elementary School Look at other dictionaries: Omnitruncated 5-simplex honeycomb — (No image) Type Uniform honeycomb Family Omnitruncated simplectic honeycomb Schläfli symbol t0,1,2,3,4,5{3[6]} Coxeter–Dynkin diagrams …   Wikipedia Convex uniform honeycomb — The alternated cubic honeycomb is one of 28 space filling uniform tessellations in Euclidean 3 space, composed of alternating yellow tetrahedra and red octahedra. In geometry, a convex uniform honeycomb is a uniform tessellation which fills three …   Wikipedia 16-cell honeycomb — Perspective projection: the first layer of adjacent 16 cell facets. Type Regular 4 space honeycomb Family Alternated hypercube honeycomb Schläfli symbol {3,3,4,3} h{4,3,3,4} …   Wikipedia List of mathematics articles (O) — NOTOC O O minimal theory O Nan group O(n) Obelus Oberwolfach Prize Object of the mind Object theory Oblate spheroid Oblate spheroidal coordinates Oblique projection Oblique reflection Observability Observability Gramian Observable subgroup… …   Wikipedia Octagonal prism — Uniform Octagonal prism Type Prismatic uniform polyhedron Elements F = 10, E = 24, V = 16 (χ = 2) Faces by sides 8{4}+2{8} Schläfli …   Wikipedia Convex uniform honeycombs in hyperbolic space — The {5,3,4} honeycomb in 3D hyperbolic space, viewed in perspective In geometry, a convex uniform honeycomb is a tessellation of convex uniform polyhedron cells. In 3 dimensional hyperbolic space there are nine Coxeter group f …   Wikipedia Runcinated 5-cell — 5 cell …   Wikipedia Truncated octahedron — (Click here for rotating model) Type Archimedean solid Uniform polyhedron Elements F = 14, E = 36, V = 24 (χ = 2) Faces by sides 6 …   Wikipedia Alternation (geometry) — In geometry, an alternation (also called partial truncation ) is an operation on a polyhedron or tiling that fully truncates alternate vertices. Only even sided polyhedra can be alternated, for example the zonohedra. Every 2n sided face becomes n …   Wikipedia Uniform polytope — A uniform polytope is a vertex transitive polytope made from uniform polytope facets. A uniform polytope must also have only regular polygon faces.Uniformity is a generalization of the older category semiregular, but also includes the regular… …   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”