Demihypercube

Alternation of the n-cube yields one of two n-demicubes, as in this 3-dimensional illustration of the two tetrahedra that arise as the 3-demicubes of the 3-cube.

The rhombic disphenoid inside of a cuboid

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_n for being half of the hypercube family, γ_n. 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.

单词	Demihypercube
释义	Demihypercube 英语百科 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_n for being half of the hypercube family, γ_n. 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.
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