Small tetrisicositetrachoron

The small tetrisicositetrachoron, or suti, is a nonconvex uniform polychoron that consists of 24 truncated octahedra, 24 quasitruncated hexahedra, 24 small rhombicuboctahedra, and 24 quasitruncated cuboctahedra. 1 quasitruncated hexahedron, 1 truncated octahedron, 1 small rhombicuboctahedron, and 2 quasitruncated cuboctahedra join at each vertex.

The small tetrisicositetrachoron contains the vertices of a tesseractihexadecaquasitruncated prismatotesseractihexadecachoron.

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


 * $$\left(±\frac{2-\sqrt2}{2},\,±\sqrt2,\,±\frac{\sqrt2}{2},\,0\right),$$
 * $$\left(±\frac{2\sqrt2-1}{2},\,±\frac{\sqrt2-1}{2},\,±\frac{1+\sqrt2}{2},\,±\frac12\right).$$

The second set of vertices are identical to the vertices of an inscribed tesseractihexadecaquasitruncated prismatotesseractihexadecachoron.

Related polychora
The small tetrisicositetrachoron is the colonel of a 3-member regiment that also includes the disicositetraquasitruncated disicositetrachoron and small rhombic trisicositetrachoron.