Small skewverted prismatohexadecadisoctachoron

The small skewverted prismatohexadecadisoctachoron, or skiviphado, is a nonconvex uniform polychoron that consists of 24 octagrammic prisms, 16 cuboctahedra, 8 small rhombicuboctahedra, and 8 great cubicuboctahedra. 1 cuboctahedron, 1 small rhombicuboctahedron, 1 great cubicuboctahedron, and 2 octagrammic prisms join at each vertex.

The small skewverted prismatohexadecadisoctachoron contains the vertices of a cuboctatruncated cuboctahedral prism and octagonal-octagrammic duoprism, and can be vertex-inscribed into the antifrustary distetracontoctachoron.

Vertex coordinates
The vertices of a small skewverted prismatohexadecadisoctachoron of edge length 1 are given by all permutations of:


 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac12,\,±\frac12,\,±\frac{\sqrt2-1}{2}\right).$$