Tetrahedral-octahedral honeycomb

﻿
Tetrahedral-octahedral honeycomb

The tetrahedral-octahedral honeycomb or alternated cubic honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space. It is comprised of alternating octahedra and tetrahedra in a ratio of 1:2.

It is vertex-transitive with 8 tetrahedra and 6 octahedra around each vertex. It is edge-transitive with 2 tetrahedra and 2 octahedra alternating on each edge.

It is part of an infinite family of uniform tessellations called demihypercubic tessellations, formed as an alternation of a hypercubic honeycomb and being composed of demihypercube and cross-polytope facets.

In this case of 3-space, the cubic honeycomb is alternated, reducing the cubic cells to tetrahedra, and the deleted vertices create octahedral voids. As such it can be represented by an extended Schläfli symbol h{4,3,4} as containing "half" the vertices of the {4,3,4} cubic honeycomb.

There's a similar honeycomb called gyrated tetrahedral-octahedral honeycomb which has layers rotated 60 degrees so half the edges have neighboring rather than alternating tetrahedra and octahedra.

Images

ee also

*cubic honeycomb

Wikimedia Foundation. 2010.

Look at other dictionaries:

• Gyrated tetrahedral-octahedral honeycomb — The gyrated tetrahedral octahedral honeycomb or gyrated alternated cubic honeycomb is a space filling tessellation (or honeycomb) in Euclidean 3 space made up of octahedra and tetrahedra in a ratio of 1:2.It is vertex uniform with 8 tetrahedra… …   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

• Alternated hypercubic honeycomb — An alternated square tiling is another square tiling, but having two types of squares, alternating in a checkerboard pattern …   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

• Semiregular 4-polytope — In geometry, a semiregular 4 polytope (or polychoron) is a 4 dimensional polytope which is vertex transitive (i.e. the symmetry group of the polytope acts transitively on the vertices) and whose cells are regular polyhedra. These represent a… …   Wikipedia

• List of mathematics articles (T) — NOTOC T T duality T group T group (mathematics) T integration T norm T norm fuzzy logics T schema T square (fractal) T symmetry T table T theory T.C. Mits T1 space Table of bases Table of Clebsch Gordan coefficients Table of divisors Table of Lie …   Wikipedia

• Octahedron — For the album by The Mars Volta, see Octahedron (album). Regular Octahedron (Click here for rotating model) Type Platonic solid Elements F = 8, E = 12 V = 6 (χ = 2) Faces by sides …   Wikipedia

• Nid d'abeille (géométrie) — Pour Nid d’abeille, voir Nid d abeille (homonymie). En géométrie, un nid d’abeille est le nom donné pour un pavage remplissant l’espace par des polyèdres, de la même manière qu’un pavage remplit un plan par des polygones. Le terme pavage est… …   Wikipédia en Français

• List of mathematics articles (G) — NOTOC G G₂ G delta space G networks Gδ set G structure G test G127 G2 manifold G2 structure Gabor atom Gabor filter Gabor transform Gabor Wigner transform Gabow s algorithm Gabriel graph Gabriel s Horn Gain graph Gain group Galerkin method… …   Wikipedia

• Coxeter group — In mathematics, a Coxeter group, named after H.S.M. Coxeter, is an abstract group that admits a formal description in terms of mirror symmetries. Indeed, the finite Coxeter groups are precisely the finite Euclidean reflection groups; the symmetry …   Wikipedia