Celliprismated penteract

The celliprismated penteract, or cappin, also called the steritruncated 5-orthoplex, is a convex uniform polyteron. It consists of 40 tesseracts, 80 square-hexagonal duoprisms, 80 truncated tetrahedral prisms, 32 rectified pentachora, and 10 small disprismatotesseractihexadecachoron. 1 small disprismatotesseractihexadecachoron, 1 tesseract, 1 truncated pentachoron, 3 truncated tetrahedral prisms, and 3 square-hexagonal duoprisms join at each vertex. As the name suggests, it is the steritruncation of the triacontaditeron.

The celliprismated penteract contains the vertices of a prismatorhombated tesseractic prism and square-great rhombicuboctahedral duoprism.

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