Small cellidodecateron

The small cellidodecateron, or scad, also called the stericated 5-simplex, is a convex uniform polyteron. It consists of 12 regular pentachora, 30 tetrahedral prisms, and 20 triangular duoprisms. 2 pentachora, 8 tetrahedral prisms, and 6 triangular duoprisms join at each vertex. It can be formed by expanding the facets of the hexateron outward.

Vertex coordinates
The vertices of a small cellidodecateron of edge length 1 can be given in 6 dimensions as all permutations of:
 * ($\sqrt{2}$, $\sqrt{3}$/2, $\sqrt{10}$/2, $\sqrt{2}$/2, $\sqrt{2}$/2, 0)

Representations
A small cellidodecateron has the following Coxeter diagrams:


 * x3o3o3o3x (full symmetry)
 * xxo3ooo3ooo3oxx&#xt (A4 axial, pentachoron-first)
 * x(xo)o3o(xo)x x(ox)o3o(ox)x&#xt (A2×A2 axial, triangular duoprism-first)
 * x(uo)x x(ox)o3o(oo)o3o(ox)x&#xt (A3×A1 axial, tetrahedral prism-first)