Tetrahedral-octahedral honeycomb
quasiregular space-filling tesselation
The tetrahedral-octahedral honeycomb, alternated cubic honeycomb is a quasiregular space-filling tessellation (or honeycomb) in Euclidean 3-space. It is composed of alternating regular octahedra and tetrahedra in a ratio of 1:2.
Other names include half cubic honeycomb, half cubic cellulation, or tetragonal disphenoidal cellulation. John Horton Conway called this honeycomb a tetroctahedrille, and its dual a dodecahedrille.
R. Buckminster Fuller combined the two words octahedron and tetrahedron into octet truss, a rhombohedron consisting of one octahedron (or two square pyramids) and two opposite tetrahedra.
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. The vertex locations of the tetrahedral-octahedral honeycomb produce the face-centered cubic (FCC) lattice in crystals.
A geometric honeycomb is a space-filling of polyhedral or higher-dimensional cells, so that there are no gaps. It is an example of the more general mathematical tiling or tessellation in any number of dimensions.
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