Hypercubic honeycomb
Regular tilings of ≥3D spaces with hypercubes / From Wikipedia, the free encyclopedia
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.
![]() 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 δn+1 for an n-dimensional honeycomb.