Great prismatotetracontoctachoron

The great prismatotetracontoctachoron, or gippic, also commonly called the omnitruncated 24-cell, is a convex uniform polychoron that consists of 192 hexagonal prisms and 48 great rhombicuboctahedra. 2 hexagonal prisms and 2 great rhombicuboctahedra join at each vertex. It is the omnitruncate of the F4 family of uniform polychora.

This polychoron can be alternated into a snub tetracontoctachoron, although it cannot be made uniform.

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


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

Representations
A great prismatotetracontoctachoron has the following Coxeter diagrams:


 * x3x4x3x (full symmetry)
 * xux4wxx3xxx3xwX&#zx (BC4 symmetry)

Semi-uniform variant
The great prismatotetracontoctachoron has a semi-uniform variant of the form x3y4y3x that maintains its full symmetry. This variant uses 48 great rhombicuboctahedra of form y4y3x and 192 ditrigonal prisms of form x x3y as cells, with 2 edge lengths.

With edges of length a and b (so that it is represented by a3b4b3a), its circumradius is given by $$\sqrt{2a^2+6b^2+6ab+(a^2+4b^2+4ab)\sqrt2}$$.

If it has only single icositetrachoric symmetry, the variant is called a great disprismatoicositetricositetrachoron.