Order-6 tetrahedral honeycomb

It is paracompact because it has vertex figures composed of an infinite number of faces, and has all vertices as ideal points at infinity.

With Schläfli symbol {3,3,6}, the order-6 tetrahedral honeycomb has six ideal tetrahedra around each edge.

[1] A geometric honeycomb is a space-filling of polyhedral or higher-dimensional cells, so that there are no gaps.

The order-6 tetrahedral honeycomb is analogous to the two-dimensional infinite-order triangular tiling, {3,∞}.

The rectified order-6 tetrahedral honeycomb, t1{3,3,6} has octahedral and triangular tiling cells arranged in a hexagonal prism vertex figure.