Great quasicellipenteractitriacontaditeron

The great quasicellipenteractitriacontaditeron or great quasicellated penteractitriacontaditeron, short name gaquacint, is a nonconvex uniform polyteron. It consists of 80 hexagonal-octagrammic duoprisms, 80 truncated octahedral prisms, 40 quasitruncated cuboctahedral prisms, 32 great prismatodecachora, and 10 great quasidisprismatotesseractihexadecachora. One of each type of facet joins at each vertex. It is the quasiomnitruncation of the penteract.

Vertex coordinates
The vertices of a great quasicellipenteractitriacontaditeron of edge length 1 are given by all permutations of:
 * $$\left(±\frac{4\sqrt2-1}{2},\,±\frac{3\sqrt2-1}{2},\,±\frac{2\sqrt2-1}{2},\,±\frac{\sqrt2-1}{2},\,±\frac12\right).$$