- Tetrahedral-octahedral honeycomb
The

**tetrahedral-octahedral honeycomb**or**alternated cubic honeycomb**is a space-fillingtessellation (or honeycomb) inEuclidean 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 andcross-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 extendedSchläfli 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

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