Small prismatodemipenteract

The small prismated demipenteract, 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 cellated penteractitriacontaditeron, or by expanding the hexadecachoric facets of the demipenteract outwards.

Vertex coordinates
The vertices of a small prismated demipenteract 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 prismated demipenteract has the following Coxeter diagrams:


 * x3o3o *b3o3x (full symmetry)
 * s4o3o3o3x (as alternated faceting)
 * xxoo3oooo3ooxx *b3oxxo&#xt (D4 axial, hexadecachoron-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)