Related Families of Polytopes
The hypercubes are one of the few families of regular polytopes that are represented in any number of dimensions.
The hypercube (offset) family is one of three regular polytope families, labeled by Coxeter as γn. The other two are the hypercube dual family, the cross-polytopes, labeled as βn, and the simplices, labeled as αn. A fourth family, the infinite tessellations of hypercubes, he labeled as δn.
Another related family of semiregular and uniform polytopes is the demihypercubes, which are constructed from hypercubes with alternate vertices deleted and simplex facets added in the gaps, labeled as hγn.
Read more about this topic: Hypercube
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