Small prismated penteract

The small prismated penteract, or span, also called the runcinated 5-cube, is a convex uniform polyteron. It consists of 80 triangular-square duoprisms, 80 octahedral prisms, 32 rectified pentachora, and 10 small disprismatotesseractihexadecachoron. One rectified pentachoron, 2 small disprismatotesseractihexadecachora, 3 octahedral prisms, and 3 triangular-square duoprisms join at each vertex. As the name suggests, it is the runcination of the penteract.

The small prismated penteract contains the vertices of a small rhombated tesseractic prism, square-truncated cubic duoprism, octagonal-small rhombicuboctahedral duoprism, and octagonal duoprismatic prism.

Vertex coordinates
The vertices of a small prismated penteract of edge length 1 are given by all permutations of:
 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac{1+\sqrt2}{2},\,±\frac12,\,±\frac12,\,±\frac12\right).$$

Representations
A small prismated penteract has the following Coxeter diagrams:


 * x4o3o3x3o (full symmetry)
 * xxxx4oooo3oxxo3xoox&#xt (BC4 axial, small disprismatotesseractihexadecachoron-first)
 * wx xx4oo3ox3xo&#zx (BC4×A1 symmetry)
 * wxx4oxo oxo3oox4xxx&#zxt (BC3×BC2 symmetry)

Related polytopes
The regiment of the small prismated penteract includes a total of 37 members plus one fissary member.