The tetrahedral-octahedral honeycomb, also called the alternated cubic honeycomb, is the quasiregular honeycomb of three-dimensional Euclidean space whose cells are regular tetrahedra and regular octahedra (Coxeter 1940, 1973).
Eight tetrahedra and six octahedra meet at every vertex, so the vertex figure is a
cuboctahedron. Double-counting vertex-cell incidences
in a periodic repeat unit shows that the numbers of tetrahedral and octahedral cells
occur in the ratio 
. At every polyhedron edge,
two tetrahedra and two octahedra
meet. This is possible because their dihedral angles
are 
and 
,
whose sum is 
.
Its vertex set is the face-centered cubic lattice, and the corresponding Voronoi cells are rhombic dodecahedra. One regular
octahedron together with the eight regular tetrahedra
attached to its faces forms a stella octangula.
Finite slabs of its 
-skeleton are used as octet
trusses.
