Demipenteract

The demipenteract, or hin, also called the hemipenteract or 5-demicube, is a convex uniform polyteron. It has 10 hexadecachora and 16 pentachora as facets, with 5 of each at a vertex forming a rectified pentachoron as the vertex figure. It is the 5-dimensional demihypercube and is formed by alternating the penteract.

This is the lowest-dimensional demihypercube that is not identical to another regular polytope of the same dimension.

It is also a convex segmentoteron, as a hexadecachoron atop rotated hexadecachoron, or hexadecachoric alterprism. It is also the digonal-tetrahedral duoantiprism.

Vertex coordinates
The vertices of a demipenteract of edge length 1, centered at the origin, are given by all even sign changes of:
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}\right).$$

Representations
A demipenteract has the following Coxeter diagrams:


 * x3o3o *b3o3o (full symmetry)
 * s4o3o3o3o (as alternated penteract)
 * xo3oo3ox *b3oo&#x (D4 axial, demitesseractic alterprism)
 * ooo3oxo3ooo3oox&#xt (A4 axial, vertex-first)
 * xox3ooo3oxo oxo&#xt (A3×A1 axial, tetrahedron-first)
 * xo3oo3ox xo ox&#zx (A3×A1×A1 symmetry)
 * xoxo oxox oxoo3ooxo&#xt (A2×A1×A1 axial, edge-first)

Related polytopes
The demipenteract is the colonel of a 6-member regiment. Its other members include the dishexadecateron, hexadecapenteract, retrodishexadecateron, retropenteractihexadecateron, and the noble hexadecateron.

The hollow stellated icositetrachoric antiprism can be constructed as a blend of 6 demipenteracts.