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
Snub 24-cell honeycomb Snub 24-cell honeycomb In four-dimensional Euclidean geometry, the snub 24-cell honeycomb, or snub icositetrachoric honeycomb is a uniform space-filling tessellation (or honeycomb) by snub 24-cells, 16-cells, and 5-cells. It was discovered by Thorold Gosset with his 1900 paper of semiregular polytopes. It is not semiregular by Gosset's definition of regular facets, but all of its cells (ridges) are regular, either tetrahedra or icosahedra. It can be seen as an alternation of a truncated 24-cell honeycomb, and can be represented by Schläfli symbol s{3,4,3,3}, s{3}, and 3 other snub constructions. It is defined by an irregular decachoron vertex figure (10-celled 4-polytope),