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:
 * $$\left(±\frac{3\sqrt2}{2},\,±\sqrt2,\,±\sqrt2,\,±\frac{\sqrt2}{2},\,0\right).$$

Representations
A prismatorhombated triacontaditeron has the following Coxeter diagrams:


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

Related polytopes
The prismatorhombated triacontaditeron is the colonel of a three-member regiment that also includes the retroprismatorhombated triacontaditeron and lepidoprismatorhombated triacontaditeron.