Penteractiquasirhombated penteractitriacontaditeron

The penteractiquasirhombated penteractitriacontaditeron, or noqrant, is a nonconvex uniform polyteron. It consists of 10 tesseractihexadecaquasitruncated prismatotesseractihexadecachora, 32 great rhombated pentachora, 10 great quasirhombated tesseracts, and 80 triangular-octagonal duoprisms. One great rhombated pentachoron, 1 great quasirhombated tesseract, 1 triangular-octagonal duoprism, and 2 tesseractihexadecaquasitruncated prismatotesseractihexadecachora join at each vertex.

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