Quasicelliprismatotruncatopenteractitriacontaditeron

The quasicelliprismatotruncatopenteractitriacontaditeron or quasicelliprismatotruncated penteractitriacontaditeron, short name quicpatint, is a nonconvex uniform polyteron. It consists of 80 truncated tetrahedral prisms, 80 hexagonal-octagrammic duoprisms, 40 quasitruncated hexahedral prisms, 32 prismatorhombated pentachora, and 10 quasiprismatorhombated hexadecachora. 1 prismatorhombated pentachoron, 1 quasiprismatorhombated hexadecachoron, 1 truncated tetrahedral prism, 1 quasitruncated hexahedral prism, and 2 hexagonal-octagrammic duoprisms join at each vertex. It is the quasisteriruncitruncation of the penteract.

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

Related polytopes
The quasicelliprismatotruncatopenteractitriacontaditeron is the colonel of a three-member regiment that also includes the great retrocelliprismatotruncatopenteractitriacontaditeron and great lepidocelliprismatotruncatopenteractitriacontaditeron.