Prismatotruncated triacontaditeron

The prismatotruncated triacontaditeron, or pattit, also called the runcitruncated 5-orthoplex, is a convex uniform polyteron. It consists of 80 square-hexagonal duoprisms, 40 cuboctahedral prisms, 10 rectified icositetrachora, and 32 prismatorhombated pentachora. One rectified icositetrachoron, 1 cuboctahedral prism, 2 prismatorhombated pentachora, and 2 square-hexagonal duoprisms join at each vertex. As the name suggests, it is the runcitruncation of the triacontaditeron.

Vertex coordinates
The vertices of a prismatotruncated triacontaditeron of edge length 1 are given by all permutations of:
 * $$\left(±\frac{3\sqrt2}{2},\,±\sqrt2,\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0\right).$$

Representations
A prismatotruncated triacontaditeron has the following Coxeter diagrams:


 * o4x3o3x3x (full symmetry)
 * x3o3x *b3x3x (D5 symmetry)
 * s4x3o3x3x (D5 symmetry, as alternated faceting)