Sphenoverted trisicositetrachoron

The sphenoverted trisicositetrachoron, or wavaty, is a nonconvex uniform polychoron that consists of 24 cuboctahedra, 24 quasitruncated hexahedra, and 24 great cubicuboctahedra. 1 cuboctahedron, 2 quasitruncated hexahedra, and 2 great cubicuboctahedra join at each vertex.

The sphenoverted trisicositetrachoron contains the vertices of a quasiprismatorhombated hexadecachoron.

Vertex coordinates
The vertices of a sphenoverted trisicositetrachoron of edge length 1 are given by all permutations of:


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

The second set of vertices are identical to those of an inscribed quasiprismatorhombated hexadecachoron.

The polychoron in dual F4 symmetry has vertex coordinates given by all permutations of:


 * $$\left(±\frac{2-\sqrt2}{2},\,±\frac{2-\sqrt2}{2},\,±1,\,0\right),$$
 * $$\left(±\frac{3-\sqrt2}{2},\,±\frac{\sqrt2-1}{2},\,±\frac12,\,±\frac12\right).$$

Related polychora
The sphenoverted trisicositetrachoron is the colonel of a 7-member regiment. Its other members include the quasirhombated icositetrachoron, great rhombic disicositetrachoron, great pseudorhombic disicositetrachoron, grand quasirhombic disicositetrachoron, prismatoicositetrintercepted disicositetrachoron, and icositetrintercepted trisicositetrachoron.