Penteractiquasiprismatotruncated penteractitriacontaditeron

The penteractiquasiprismatotruncated penteractitriacontaditeron, or naquiptant, is a nonconvex uniform polyteron. It consists of 10 tesseractihexadecaquasitruncated tesseractihexadecachora, 10 quasiprismatorhombated hexadecachora, 32 prismatorhombated pentachora, 40 cuboctatruncated cuboctahedral prisms, and 80 triangular-octagonal duoprisms. 1 prismatorhombated pentachoron, 1 quasiprismatorhombated hexadecachoron, 1 tesseractihexadecaquasitruncated tesseractihexadecachoron, 1 triangular-octagonal duoprism, and 2 cuboctatruncated cuboctahedral prisms join at each vertex.

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

Related polytopes
The penteractiquasiprismatotruncated penteractitriacontaditeron is the colonel of a three-member regiment that also includes the penteractiquasiretroprismatotruncated penteractitriacontaditeron and penteractiquasilepidoprismatotruncated penteractitriacontaditeron.