Small prismated triacontaditeron

The small prismated triacontaditeron, or spat, also called the runcinated 5-orthoplex, is a convex uniform polyteron. It consists of 80 triangular-square duoprisms, 40 cuboctahedral prisms, 10 rectified tesseracts, and 32 small prismatodecachora. One rectified tesseract, 2 small prismatodecachora, 3 cuboctahedral prisms, and 3 triangular-square duoprisms join at each vertex. As the name suggests, it is the runcination of the triacontaditeron.

Vertex coordinates
The vertices of a small prismated triacontaditeron of edge length 1 are given by all permutations of:
 * $$\left(±\sqrt2,\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0\right).$$

Representations
A small prismated triacontaditeron has the following Coxeter diagrams:


 * o4x3o3o3x (full symmetry)
 * x3o3x *b3o3x (D5 symmetry)
 * s4x3o3o3x (D5 symmetry, as alternated faceting)
 * ooqoo4xxoxx3oooo3oxxxo&#xt (B4 axial, rectified tesseract-first)
 * xx(ox)(uo)xx3oo(ox)(xx)xo3ox(xx)(ox)oo3xx(uo)(ox)xx&#xt (A4 axial, small prismatodecachoron-first)

Related polytopes
The regiment of the small prismated triacontaditeron includes a total of 85 members plus 8 fissary members. Of these, 37 of the main members and one of the fissaries have full symmetry, while the rest have D5 symmetry only.