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
Cubic honeycomb uniform honeycombs constructed by the formula_1 Coxeter group. The symmetry can be multiplied by the symmetry of rings in the Coxeter–Dynkin diagrams: <HR> The rectified cubic honeycomb or rectified cubic cellulation is a uniform space-filling tessellation (or honeycomb) in Euclidean 3-space. It is composed of octahedra and cuboctahedra in a ratio of 1:1. John Horton Conway calls this honeycomb a cuboctahedrille, and its dual an oblate octahedrille. The "rectified cubic honeycomb" can be orthogonally projected into the euclidean plane with various symmetry arrangements. There are four uniform colorings for the cells of this honeycomb with reflective symmetry, listed by their