Small prismated hexateron

The small prismated hexateron, or spix, also called the runcinated 5-simplex, is a convex uniform polyteron. It consists of 20 triangular duoprisms, 15 octahedral prisms, 6 rectified pentachora, and 6 small prismatodecachora. One rectified pentachoron, 2 small prismatodecachora, 3 octahedral prisms, and 3 triangular duoprisms join at each vertex. As the name suggests, it is the runcination of the hexateron.

Vertex coordinates
The vertices of a small prismated hexateron of edge length 1 can be given in 6 dimensions as all permutations of:
 * $$\left(\sqrt2,\,\frac{\sqrt2}{2},\,\frac{\sqrt2}{2},\,\frac{\sqrt2}{2},\,0,\,0\right).$$

Representations
A small prismated hexateron has the following Coxeter diagrams:


 * x3o3o3x3o (full symmetry)
 * oox3xxo3ooo3oxx&#xt (A4 axial, rectified pentachoron-first)

Related polytopes
The regiment of the small prismated hexateron includes a total of 37 members plus one fissary member. This makes it the largest regiment of uniform polytera with A5 symmetry.