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 an omnisnub icositetrachoron, 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)