Order-6 hexagonal tiling honeycomb . The "cantellated order-6 hexagonal tiling honeycomb", t{6,3,6}, has trihexagonal tiling and rhombitrihexagonal tiling cells, with a triangular prism vertex figure. The "cantitruncated order-6 hexagonal tiling honeycomb", t{6,3,6}, has hexagonal tiling and truncated trihexagonal tiling cells, with a triangular prism vertex figure. The runcinated order-6 hexagonal tiling honeycomb, t{6,3,6}, has hexagonal tiling and hexagonal prism cells, with a triangular antiprism vertex figure. It is analogous to the 2D hyperbolic rhombihexahexagonal tiling, rr{6,6}, with square and hexagonal faces: The runcitruncated order-6 hexagonal tiling honeycomb, t{6,3,6}, has Truncated hexagonal tiling, rhombitrihexagonal tiling, hexagonal prism, and dodecagonal prism cells. The omnitruncated order-6 hexagonal
Cubic honeycomb Cubic honeycomb The cubic honeycomb or cubic cellulation is the only regular space-filling tessellation (or honeycomb) in Euclidean 3-space, made up of cubic cells. It has 4 cubes around every edge, and 8 cubes around each vertex. Its vertex figure is a regular octahedron. It is a self-dual tessellation with Schläfli symbol {4,3,4}. John Horton Conway calls this honeycomb a cubille. The Cartesian coordinates of the vertices are: It is part of a multidimensional family of hypercube honeycombs, with Schläfli symbols of the form {4,3...,3,4}, starting with the square tiling, {4,4} in the plane. It is one of 28 uniform