Great dispenteractirhombated triacontaditeron

The great dispenteractirhombated triacontaditeron, or gadinnert, is a nonconvex uniform polyteron. It consists of 10 tesseractihexadecatruncated prismatotesseractihexadecachora, 32 great rhombated pentachora, 10 tesseractihexadecaquasitruncated tesseractihexadecachora, and 40 quasitruncated hexahedral prisms. One great rhombated pentachoron, 1 tesseractihexadecaquasitruncated tesseractihexadecachoron, 1 quasitruncated hexahedral prism, and 2 tesseractihexadecatruncated prismatotesseractihexadecachora join at each vertex.

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