Great quasirhombated icositetrachoron

The great quasirhombated icositetrachoron, or gaqri, is a nonconvex uniform polychoron that consists of 96 triangular prisms, 24 quasitruncated hexahedra, and 24 quasitruncated cuboctahedra. 1 triangular prism, 1 quasitruncated hexahedron, and 2 quasitruncated cuboctahedra join at each vertex. As the name suggests, it can be obtained by quasicantitruncating the icositetrachoron.

Vertex coordinates
The vertices of a great quasirhombated icositetrachoron of edge length 1 are given by all permutations of:


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

The quasicantitruncation of the dual icositetrachron has coordinates given by all permutations of:


 * $$\left(±\frac{5-2\sqrt2}{2},\,±\frac{\sqrt2-1}{2},\,±\frac{\sqrt2-1}{2},\,±\frac12\right),$$
 * $$\left(±\frac{3-2\sqrt2}{2},\,±\frac{3-\sqrt2}{2},\,±\frac{3-\sqrt2}{2},\,±\frac12\right),$$
 * $$\left(±(2-\sqrt2),\,±\frac{2-\sqrt2}{2},\,±\frac{2-\sqrt2}{2},\,±1\right).$$