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.](/Images/godic/202501/08/CubeAndStel.svg1844.png")
![The rhombic disphenoid inside of a cuboid](/Images/godic/202501/08/Rhombic_disphenoid1844.png")
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 2 (n-1)-simplex facets are formed in place of the deleted vertices.