Great prismatotrisicositetrachoron

The great prismatotrisicositetrachoron, or gipti, is a nonconvex uniform polychoron that consists of 96 triangular prisms, 24 truncated octahedra, 24 great cubicuboctahedra, and 24 quasitruncated cuboctahedra. 1 triangular prism, 1 truncated octahedron, 1 great cubicuboctahedron, and 2 quasitruncated cuboctahedra join at each vertex.

The great prismatotrisicositetrachoron contains the vertices of a great quasidisprismatotesseractihexadecachoron.

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


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

The second set of vertices are identical to the vertices of an inscribed great quasidisprismatotesseractihexadecachoron.

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


 * $$\left(±\frac{5-\sqrt2}{2},\,±\frac{\sqrt2-1}{2},\,±\frac12,\,±\frac12\right),$$
 * $$\left(±\frac{3-\sqrt2}{2},\,±\frac{3-\sqrt2}{2},\,±\frac32,\,±\frac12\right),$$
 * $$\left(±\frac{4-\sqrt2}{2},\,±\frac{2-\sqrt2}{2},\,±1,\,±1\right).$$

Related polychora
The great prismatotrisicositetrachoron is the colonel of a 3-member regiment that also includes the prismatoquasirhombated icositetrachoron and great rhombiprismic disicositetrachoron.