Penteractirhombated penteractitriacontaditeron

The penteractirhombated penteractitriacontaditeron, or nurrant, is a nonconvex uniform polyteron. It consists of 10 tesseractihexadecatruncated prismatotesseractihexadecachora, 32 great rhombated pentachora, 10 great rhombated tesseracts, and 80 triangular-octagrammic duoprisms. One great rhombated pentachoron, 1 great rhombated tesseract, 1 triangular-octagrammic duoprism, and 2 tesseractihexadecatruncated prismatotesseractihexadecachora join at each vertex.

Vertex coordinates
The vertices of a penteractirhombated penteractitriacontaditeron of edge length 1 are given by all permutations of:
 * $$\left(±\frac{1+2\sqrt2}{2},\,±\frac{1+2\sqrt2}{2},\,±\frac{1+\sqrt2}{2},\,±\frac{\sqrt2-1}{2},\,±\frac12\right).$$