Truncated tetrahedral honeycomb

The truncated tetrahedral honeycomb, or tath, is a paracompact uniform tiling of 3D hyperbolic space. 1 triangular tiling and 6 truncated tetrahedra meet at each vertex. It is paracompact because it has Euclidean triangular tiling cells. As the name suggests, it can be derived by truncation of the tetrahedral honeycomb.

Representations
A truncated tetrahedral honeycomb has the following Coxeter diagrams:


 * o6o3x3x (full symmetry)
 * x3x3o3o*b (half symmetry)