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
Cubic honeycomb Cubic honeycomb The cubic honeycomb or cubic cellulation is the only regular space-filling tessellation (or honeycomb) in Euclidean 3-space, made up of cubic cells. It has 4 cubes around every edge, and 8 cubes around each vertex. Its vertex figure is a regular octahedron. It is a self-dual tessellation with Schläfli symbol {4,3,4}. John Horton Conway calls this honeycomb a cubille. The Cartesian coordinates of the vertices are: It is part of a multidimensional family of hypercube honeycombs, with Schläfli symbols of the form {4,3...,3,4}, starting with the square tiling, {4,4} in the plane. It is one of 28 uniform