The order-4 octahedral honeycomb is a regular paracompact honeycomb in hyperbolic 3-space. It is paracompact because it has infinite vertex figures, with...

its dual, the order-4 octahedral honeycomb, {3,4,4}. The square tiling honeycomb is part of the order-4 square tiling honeycomb family, as it can be seen...

geometry of hyperbolic 3-space, the order-5 octahedral honeycomb is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {3,4,5}. It...

The tetrahedral-octahedral honeycomb, alternated cubic honeycomb is a quasiregular space-filling tessellation (or honeycomb) in Euclidean 3-space. It...

in an octahedral arrangement. Its vertices are constructed from 3 orthogonal axes. Its dual is the order-5 cubic honeycomb. A geometric honeycomb is a...

tiling cells: This honeycomb is also related to the 16-cell, cubic honeycomb and order-4 dodecahedral honeycomb, all of which have octahedral vertex figures...

In the geometry of hyperbolic 3-space, the cubic-octahedral honeycomb is a compact uniform honeycomb, constructed from cube, octahedron, and cuboctahedron...

and honeycombs with {p,3,4} Schläfli symbol, and octahedral vertex figures: In the geometry of hyperbolic 3-space, the order-3-4 octagonal honeycomb or...

related to the cubic honeycomb, order-4 dodecahedral honeycomb, and order-4 hexagonal tiling honeycomb which all have octahedral vertex figures. It belongs...

3-space honeycomb or 4-polytope = 0 {\displaystyle =0}  : Euclidean 3-space honeycomb < 0 {\displaystyle <0}  : Hyperbolic 3-space honeycomb These constraints...