Celligreatorhombated penteract

The celligreatorhombated triacontadtieron, or cogart, also called the stericantitruncated 5-orthoplex, is a convex uniform polyteron. It consists of 80 square-hexagonal duoprisms, 80 truncated octahedral prisms, 40 small rhombicuboctahedral prisms, 32 great rhombated pentachora, and 10 prismatorhombated tesseracts. 1 prismatorhombated tesseract, 1 small rhombicuboctahedral prism, 1 great rhombated pentachoron, 1 square-hexagonal duoprism, and 2 truncated octahedral prisms join at each vertex. As the name suggests, it is the stericantitruncation of the triacontaditeron.

The celligreatorhombated triacontaditeron contains the vertices of a great disprismatotesseractihexadecachoric prism.

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