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.
Coxeter named this family as δn+1 for an n-dimensional honeycomb.
A third form is generated by an expansion operation applied to the regular form, creating facets in place of all lower-dimensional elements.
The orthotopic honeycombs are a family topologically equivalent to the cubic honeycombs but with lower symmetry, in which each of the three axial directions may have different edge lengths.