Penteractitruncated penteractitriacontaditeron

The penteractitruncated penteractitriacontaditeron, or nottant, is a nonconvex uniform polyteron. It consists of 10 tesseractihexadecatruncated tesseractihexadecachora, 32 truncated pentachora, and 10 truncated tesseracts. One truncated pentachoron, 1 truncated tesseract, and 3 tesseractihexadecatruncated tesseractihexadecachora join at each vertex.

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