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In geometry, a hypercubic honeycomb is a family of regular honeycombs in n-dimensional spaces with the Schläfli symbols {4,3...3,4} and containing the symmetry of Coxeter group Rn 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.
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