Hypercubic honeycomb


A regular square tiling.

1 color

A cubic honeycomb in its regular form.

1 color

A checkboard square tiling

2 colors

A cubic honeycomb checkerboard.

2 colors

Expanded square tiling

3 colors

Expanded cubic honeycomb

4 colors


4 colors


8 colors

In geometry, a hypercubic honeycomb is a family of regular honeycombs (tessellations) in n-dimensional spaces with the Schläfli symbols {4,3...3,4} and containing the symmetry of Coxeter group Rn (or B~n–1) for n ≥ 3.

The tessellation is constructed from 4 n-hypercubes per ridge. The vertex figure is a cross-polytope {3...3,4}.

The hypercubic honeycombs are self-dual.

Coxeter named this family as δn+1 for an n-dimensional honeycomb.