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
Bitruncated cubic honeycomb the Coxeter–Dynkin diagrams: This honeycomb can be alternated, creating pyritohedral icosahedra from the truncated octahedra with disphenoid tetrahedral cells created in the gaps. There are three constructions from three related Coxeter-Dynkin diagrams: , , and . These have symmetry [4,3,4], [4,(3)] and [3] respectively. The first and last symmetry can be doubled as <nowiki></nowiki>4,3,4 and [[3]]. The dual honeycomb is made of cells called ten-of-diamonds decahedra. This honeycomb is represented in the boron atoms of the α-rhombihedral crystal. The centers of the icosahedra are located at the fcc positions of the lattice. Bitruncated cubic honeycomb The bitruncated cubic honeycomb is