Rectified tetrahedral honeycomb

The rectified tetrahedral honeycomb, or rath, is a paracompact uniform tiling of 3D hyperbolic space. 6 octahedra (as tetratetrahedra) and 2 triangular tilings meet at each vertex. It is paracompact because it has Euclidean triangular tiling cells. As the name suggests, it can be derived by rectification of the tetrahedral honeycomb.

Representations
A rectified tetrahedral honyecomb has the following Coxeter diagrams:


 * o6o3x3o (full symmetry)
 * o3x3o3o3*b (half symmetry)