Small prismatodemipenteract

The small prismatodemipenteract, or siphin, also called the steric 5-cube, is a convex uniform polyteron. It consists of 16 regular pentachora, 40 tetrahedral prisms, 10 hexadecachora, and 16 small prismatodecachora. 1 pentachoron, 4 tetrahedral prisms, 4 small prismatodecachora, and 1 hexadecachoron join at each vertex. It can be formed from an alternated faceting of the small cellipenteractitriacontaditeron, or by expanding the hexadecachoric facets of the demipenteract outwards.

Vertex coordinates
The vertices of a small prismatodemipenteract of edge length 1 are given by all permutations and even sign changes of:
 * $$\left(\frac{3\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}\right).$$

Representations
A small prismatodemipenteract has the following Coxeter diagrams:


 * x3o3o *b3o3x (full symmetry)
 * s4o3o3o3x (as alternated faceting)
 * xxoo3oooo3ooxx *b3oxxo&#xt (D4 axial, hexadecachoron-first)
 * xx(uo)x3oo(oo)o3ox(ox)o3oo(ox)x&#xt (A4 axial, pentachoron-first)
 * o(xx)(uo)(xx)(uo)x x(uo)(xx)(uo)(xx)o o(ox)(xo)(ou)(ox)x3x(ox)(ou)(xo)(ox)o&#xt (A2×A1×A1 axial, triangular prism-first)

Related polytopes
The regiment of the small prismatodemipenteract contains a total of 56 members as well as 20 fissaries. it is the largest regiment of uniform polytera whose colonel has demipenteractic symmetry.