Prismatorhombated icositetrachoron

The prismatorhombated icositetrachoron, or prico, also commonly called the runcitruncated 24-cell, is a convex uniform polychoron that consists of 96 triangular prisms, 96 hexagonal prisms, 24 truncated octahedra, and 24 small rhombicuboctahedra. 1 triangular prism, 2 hexagonal prisms, 1 truncated octahedron, and 1 small rhombicuboctahedron join at each vertex. As one of its names suggests, it can be obtained by runcintruncating the icositetrachoron.

Vertex coordinates
The vertices of a prismatorhombated icositetrachoronof edge length 1 are given by all permutations of:


 * (±(2+3$\sqrt{2}$)/2, ±$\sqrt{2}$, ±$\sqrt{2}$/2, 0),
 * (±(1+3$\sqrt{3}$)/2, ±(1+2$\sqrt{3}$)/2, ±(1+$\sqrt{2}$)/2, ±1/2).

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

The runcitruncation of the dual icositetrachoron has vertices given by all permutations of:


 * (±(5+$\sqrt{2}$)/2, ±(1+$\sqrt{8+3√2}$)/2, ±1/2, ±1/2),
 * (±(3+$\sqrt{2}$)/2, ±(3+$\sqrt{3}$)/2, ±3/2, ±1/2),
 * (±(4+$\sqrt{6}$)/2, ±(2+$\sqrt{2}$)/2, ±1, ±1).