Hexagonal tiling honeycomb

The hexagonal tiling honeycomb, also known as the order-3 hexagonal tiling honeycomb, is a paracompact regular tiling of 3D hyperbolic space. Each cell is a hexagonal tiling whose vertices lie on a horosphere, a surface in hyperbolic space that approaches a single ideal point at infinity. 3 hexagonal tilings meet at each edge, and 4 meet at each vertex.

It can be seen as a truncated triangular tiling honeycomb or bitruncated order-6 hexagonal tiling honeycomb.

This honeycomb can be alternated into an alternated hexagonal tiling honeycomb, which is uniform.

Representations
The hexagonal tiling honeycomb has the following Coxeter diagrams:


 * x6o3o3o (full symmetry)
 * x3x6o3o (as truncated triangular tiling honeycomb)
 * o6x3x6o (as bitruncated order-6 hexagonal tiling honeycomb)
 * o6x3x3x3*b (half symmetry of bitruncated order-6 hexagonal tiling honeycomb)
 * x3x3x3x3*a3*c *b3*d (quarter symmetry of bitruncated order-6 hexagonal tiling honeycomb)