Prismatorhombated triacontaditeron

The prismatorhombated triacontaditeron, or pirt, also called the runcicantellated 5-orthoplex, is a convex uniform polyteron. It consists of 80 triangular-square duoprisms, 40 truncated octahedral prisms, 10 tesseractihexadecachora, and 32 prismatorhombated pentachora. 2 prismatorhombated pentachora, 1 tesseractihexadecachoron, 1 triangular-square duoprism, and 2 truncated octahedral prisms join at each vertex. As the name suggests, it is the runcicantellation of the triacontaditeron.

Vertex coordinates
The vertices of a prismatorhombated triacontaditeron of edge length 1 are given by all permutations of:
 * (±3$\sqrt{2}$/2, ±$\sqrt{2}$, ±$\sqrt{2}$, ±$\sqrt{3}$/2, 0)

Representations
A prismatorhombated triacontaditeron has the following Coxeter diagrams:


 * o4x3x3o3x (full symmetry)
 * x3x3x *b3o3x (D5 symmetry)
 * s4x3x3o3x (D5 symmetry, as alternated faceting)