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
Order-5 dodecahedral honeycomb The runcitruncated order-5 dodecahedral honeycomb, , has truncated dodecahedron, icosidodecahedron and pentagonal prism cells, with a distorted square pyramid vertex figure. The omnitruncated order-5 dodecahedral honeycomb, , has truncated icosidodecahedron and decagonal prism cells, with a disphenoid vertex figure. Order-5 dodecahedral honeycomb The order-5 dodecahedral honeycomb is one of four compact regular space-filling tessellations (or honeycombs) in hyperbolic 3-space. With Schläfli symbol {5,3,5}, it has five dodecahedral cells around each edge, and each vertex is surrounded by twenty dodecahedra. Its vertex figure is a regular icosahedron. The dihedral angle of a Euclidean regular dodecahedron is ~116.6°, so no more than