Order-6 tetrahedral honeycomb order-6 tetrahedral honeycomb, t{3,3,6} has octahedral and triangular tiling cells connected in a hexagonal prism vertex figure. The truncated order-6 tetrahedral honeycomb, t{3,3,6} has truncated tetrahedra and triangular tiling cells connected in a hexagonal prism vertex figure. The cantellated order-6 tetrahedral honeycomb, t{3,3,6} has cuboctahedron and trihexagonal tiling cells connected in a tetrahedron vertex figure. The cantitruncated order-6 tetrahedral honeycomb, t{3,3,6} has truncated cuboctahedron and trihexagonal tiling cells connected in an octahedron vertex figure. Order-6 tetrahedral honeycomb In the geometry of hyperbolic 3-space, the order-6 tetrahedral honeycomb is a paracompact regular space-filling tessellation (or honeycomb). It is called "paracompact" because
Tetrahedral-octahedral honeycomb the vertex arrangement of the disphenoid tetrahedral honeycomb, dual honeycomb of the uniform bitruncated cubic honeycomb: It is also the body centered cubic, the union of two cubic honeycombs in dual positions. The kissing number of the D lattice is 8 and its Voronoi tessellation is a bitruncated cubic honeycomb, , containing all truncated octahedral Voronoi cells, . The [4,3,4], , Coxeter group generates 15 permutations of uniform honeycombs, 9 with distinct geometry including the alternated cubic honeycomb. The expanded cubic honeycomb (also known as the runcinated tesseractic honeycomb) is geometrically identical to the cubic honeycomb. The [4,3], , Coxeter