Square tiling honeycomb hexagonal prism, octagonal prism facets, with a tetrahedron vertex figure. The alternated omnitruncated square tiling honeycomb (or omnisnub square tiling honeycomb), h(t{4,4,3}), has snub square tiling, snub cube, triangular antiprism, square antiprism, and tetrahedron cells, with an irregular vertex figure. The alternated square tiling honeycomb is a paracompact uniform honeycomb in hyperbolic 3-space, composed of cube, and square tiling facets in a cuboctahedron vertex figure. The alternated rectified square tiling honeycomb is a paracompact uniform honeycomb in hyperbolic 3-space. Square tiling honeycomb In the geometry of hyperbolic 3-space, the square tiling honeycomb, is one of 11 paracompact regular honeycombs. It
Honeycomb (geometry) The tetrahedral-octahedral honeycomb and gyrated tetrahedral-octahedral honeycombs are generated by 3 or 2 positions of slab layer of cells, each alternating tetrahedra and octahedra. An infinite number of unique honeycombs can be created by higher order of patterns of repeating these slab layers. A honeycomb having all cells identical within its symmetries is said to be cell-transitive or isochoric. In the 3-dimensional euclidean space, a cell of such a honeycomb is said to be a "space-filling polyhedron". A necessary condition for a polyhedron to be a space-filling polyhedron is that its Dehn invariant must be zero, ruling out any of