What is "demihypercube"

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 hγ for being half of the hypercube family, γ. Half of the vertices are deleted and new facets are formed. The 2n facets become 2n (n-1)-demicubes, and 2(n-1)-simplex facets are formed in place of the deleted vertices.

They have been named with a demi- prefix to each hypercube name: demicube, demitesseract, etc. The demicube is identical to the regular tetrahedron, and the demitesseract is identical to the regular 16-cell. The demipenteract is considered semiregular for having only regular facets. Higher forms don't have all regular facets but are all uniform polytopes.

The vertices and edges of a demihypercube form two copies of the halved cube graph.