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 cubic honeycomb form: It is in a sequence of polychora and honeycomb with icosahedron vertex figures: It in a sequence of regular polychora and honeycombs with cubic cells. The first polytope in the sequence is the tesseract, and the second is the Euclidean cubic honeycomb. The rectified order-5 cubic honeycomb, , has alternating icosahedron and cuboctahedron cells, with a pentagonal prism vertex figure. There are four rectified compact regular honeycombs: The truncated order-5 cubic honeycomb, , has truncated cube and icosahedron cells, with a pentagonal pyramid vertex figure. It can be seen as analogous to the 2D hyperbolic truncated order-5 square tiling,