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- Tetrahedral-octahedral_honeycomb abstract "The tetrahedral-octahedral honeycomb or alternated cubic honeycomb or half cubic honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space. It is composed 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.John Horton Conway calls this honeycomb a Tetroctahedrille, and its dual dodecahedrille.It is part of an infinite family of uniform tessellations called alternated hypercubic honeycombs, 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.".
- Tetrahedral-octahedral_honeycomb thumbnail Alternated_cubic_tiling.png?width=300.
- Tetrahedral-octahedral_honeycomb wikiPageExternalLink UniformHoneycombs.html.
- Tetrahedral-octahedral_honeycomb wikiPageExternalLink productCd-0471010030.html.
- Tetrahedral-octahedral_honeycomb wikiPageExternalLink entI=706963.html.
- Tetrahedral-octahedral_honeycomb wikiPageID "3735260".
- Tetrahedral-octahedral_honeycomb wikiPageRevisionID "606731466".
- Tetrahedral-octahedral_honeycomb hasPhotoCollection Tetrahedral-octahedral_honeycomb.
- Tetrahedral-octahedral_honeycomb subject Category:Honeycombs_(geometry).
- Tetrahedral-octahedral_honeycomb subject Category:Polychora.
- Tetrahedral-octahedral_honeycomb comment "The tetrahedral-octahedral honeycomb or alternated cubic honeycomb or half cubic honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space. It is composed of alternating octahedra and tetrahedra in a ratio of 1:2.It is vertex-transitive with 8 tetrahedra and 6 octahedra around each vertex.".
- Tetrahedral-octahedral_honeycomb label "Tetrahedral-octahedral honeycomb".
- Tetrahedral-octahedral_honeycomb sameAs m.09y1wm.
- Tetrahedral-octahedral_honeycomb sameAs Q7706516.
- Tetrahedral-octahedral_honeycomb sameAs Q7706516.
- Tetrahedral-octahedral_honeycomb wasDerivedFrom Tetrahedral-octahedral_honeycomb?oldid=606731466.
- Tetrahedral-octahedral_honeycomb depiction Alternated_cubic_tiling.png.
- Tetrahedral-octahedral_honeycomb isPrimaryTopicOf Tetrahedral-octahedral_honeycomb.