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
Tetrahedral-octahedral honeycomb an octahedron at one end and a tetrahedron at the other. It is one of 28 convex uniform honeycombs. It has a "gyrated" form called the gyroelongated alternated cubic honeycomb with the same arrangement of cells at each vertex. Tetrahedral-octahedral honeycomb The tetrahedral-octahedral honeycomb, alternated cubic honeycomb is a quasiregular space-filling tessellation (or honeycomb) in Euclidean 3-space. It is composed of alternating octahedra and tetrahedra in a ratio of 1:2. Other names include half cubic honeycomb, half cubic cellulation, or tetragonal disphenoidal cellulation. John Horton Conway calls this honeycomb a tetroctahedrille, and its dual a dodecahedrille. It is vertex-transitive with