Order-4 dodecahedral honeycomb and order-4 hexagonal tiling honeycomb all which have octahedral vertex figures: This honeycomb is a part of a sequence of polychora and honeycombs with dodecahedral cells: The rectified order-4 dodecahedral honeycomb, , has alternating octahedron and icosidodecahedron cells, with a cube vertex figure. There are four rectified compact regular honeycombs: The truncated order-4 dodecahedral honeycomb, , has octahedron and truncated dodecahedron cells, with a cube vertex figure. It can be seen as analogous to the 2D hyperbolic truncated order-4 pentagonal tiling, t{5,4} with truncated pentagon and square faces: The bitruncated order-4 dodecahedral honeycomb, or bitruncated order-5 cubic honeycomb, , has
Cubic honeycomb around a vertex, making a chiral octahedral symmetry that can be stacked in all 3-dimensions: Individual cells have 2-fold rotational symmetry. In 2D orthogonal projection, this looks like a mirror symmetry. The truncated square prismatic honeycomb or tomo-square prismatic cellulation is a space-filling tessellation (or honeycomb) in Euclidean 3-space. It is composed of octagonal prisms and cubes in a ratio of 1:1. It is constructed from a truncated square tiling extruded into prisms. It is one of 28 convex uniform honeycombs. <HR> The snub square prismatic honeycomb or simo-square prismatic cellulation is a space-filling tessellation (or honeycomb) in Euclidean 3-space.