It is paracompact because it has vertex figures composed of an infinite number of facets, with all vertices as ideal points at infinity.
Another lower-symmetry construction, [4,3*,6], of index 6, exists with a non-simplex fundamental domain, with Coxeter-Dynkin diagram .
The rectified order-6 cubic honeycomb, r{4,3,6}, has cuboctahedral and triangular tiling facets, with a hexagonal prism vertex figure.
It is similar to the 2D hyperbolic tetraapeirogonal tiling, r{4,∞}, alternating apeirogonal and square faces: The truncated order-6 cubic honeycomb, t{4,3,6}, has truncated cube and triangular tiling facets, with a hexagonal pyramid vertex figure.
It is similar to the 2D hyperbolic truncated infinite-order square tiling, t{4,∞}, with apeirogonal and octagonal (truncated square) faces: The bitruncated order-6 cubic honeycomb is the same as the bitruncated order-4 hexagonal tiling honeycomb.
The cantellated order-6 cubic honeycomb, rr{4,3,6}, has rhombicuboctahedron, trihexagonal tiling, and hexagonal prism facets, with a wedge vertex figure.
A half-symmetry construction from the form {4,3[3]} exists, with two alternating types (colors) of triangular tiling cells.
Another lower-symmetry form of index 6, [4,3*,6], exists with a non-simplex fundamental domain, with Coxeter-Dynkin diagram .