Great rhombated icositetrachoron

The great rhombated icositetrachoron, or grico, also commonly called the cantitruncated 24-cell, is a convex uniform polychoron that consists of 96 triangular prisms, 24 truncated cubes, and 24 great rhombicuboctahedra. 1 triangular prism, 1 truncated cube, and 2 great rhombicuboctahedra join at each vertex. As one of its names suggests, it can be obtained by cantitruncating the icositetrachoron.

Vertex coordinates
The vertices of a great rhombated icositetrachoron of edge length 1 are given by all permutations of:
 * (±3(1+$\sqrt{2}$)/2, ±(1+2$\sqrt{3}$)/2, ±(1+$\sqrt{2+√2}$)/2, ±1/2),
 * (±(2+3$\sqrt{10+6√2}$)/2, ±(1+$\sqrt{2}$)/2, ±(2+$\sqrt{6}$)/2, 0).

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


 * (±(5+2$\sqrt{2}$)/2, ±(1+$\sqrt{2}$)/2, ±(1+$\sqrt{2}$)/2, ±1/2),
 * (±(3+2$\sqrt{2}$)/2, ±(3+$\sqrt{2}$)/2, ±(3+$\sqrt{2}$)/2, ±1/2),
 * (±(2+$\sqrt{2}$), ±(2+$\sqrt{2}$)/2, ±(2+$\sqrt{2}$)/2, ±1).

Representations
A great rhombated icositetrachoron has the following COxeter diagrams:


 * x3x4x3o (full symmetry)
 * xo4xw3xx3wx&#zx (BC4 symmetry)
 * xux4wxx3ooo3xwX (BC4 symmetry, dual ico)