Hypercubic honeycomb

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 $R n$ (or $B ~ n -1$ ) for $n \geq 3$ .

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

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 $δ n+1$ for an $n$ -dimensional honeycomb.

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