Uniform polytopes

thumb|Alternation (geometry)|Alternation of the yields one of two , as in this illustration of the two [[tetrahedra that arise as the of the .]] In geometry, demihypercubes (also called n-demicubes, n-hemicubes, and half measure polytopes) are a class of n-polytopes constructed from alternation of an n-hypercube, labeled as hγn for being half of the hypercube family, γn. Half of the vertices are deleted and new facets are formed. The 2n facets become 2n '(n − 1)-demicubes', and 2n '(n − 1)-simplex' facets are formed in place of the deleted vertices.

polytope that is vertex-uniform and has all its facets being regular polytopes