Small skewtrigonary biprismatocellidispenteractitriacontaditeron

The small skewtrigonary biprismatocellidispenteractitriacontaditeron, or skatbacadint, is a nonconvex uniform polyteron. It consists of 10 great tesseractitesseractihexadecachora, 10 small disprismatotesseractihexadecachora, 32 small prismatodecachora, 40 great cubicuboctahedral prisms, and 80 triangular-octagrammic duoprisms. 1 great tesseractitesseractihexadecachoron, 1 small disprismatotesseractihexadecachoron, 1 small prismatodecachoron, 3 great cubicuboctahedral prisms, and 3 triangular-octagrammic duoprisms meet at each vertex.

A small skewtrigonary biprismatocellidispenteractitriacontaditeron contains the vertices and edges of an octagrammic-small rhombicuboctahedral duoprism, an octagonal-great cubicuboctahedral duoprism, a small skewverted prismatohexadecadisoctachoric prism, a square-cuboctatruncated cuboctahedral duoprism, and an octagonal-octagrammic duoprismatic prism.

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

Related polytopes
The small skewwtrigonary biprismatocellidispenteractitriacontaditeron is the colonel of a regiment that contains 133 members plus 15 fissaries. This is the largest uniform regiment where all members have full penteractic symmetry.