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:
 * (±(5+3$\sqrt{2}$)/2, ±(1+2$\sqrt{3}$)/2, ±(1+$\sqrt{2+√2}$)/2, ±1/2),
 * (±3(1+$\sqrt{14+9√2}$)/2, ±(3+2$\sqrt{2}$)/2, ±(3+$\sqrt{3}$)/2, ±1/2),
 * (±(4+3$\sqrt{6}$)/2, ±(1+$\sqrt{2}$), ±(2+$\sqrt{2}$)/2, ±1).

Representations
A great prismatotetracontoctachoron has the following Coxeter diagrams:


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