In five-dimensional geometry, a demipenteract or 5-demicube is a semiregular 5-polytope, constructed from a 5-hypercube (penteract) with alternated vertices removed.
Since it was the only semiregular 5-polytope (made of more than one type of regular facets), he called it a 5-ic semi-regular.
Cartesian coordinates for the vertices of a demipenteract centered at the origin and edge length 2√2 are alternate halves of the penteract: with an odd number of plus signs.
The rows and columns correspond to vertices, edges, faces, cells and 4-faces.
Thorold Gosset identified this series in 1900 as containing all regular polytope facets, containing all simplexes and orthoplexes (5-simplices and 5-orthoplexes in the case of the 5-demicube).