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.

The truncated octahedra can be alternated into icosahedra to create the scaliform prismatorhombisnub icositetrachoron.

Vertex coordinates
The vertices of a prismatorhombated icositetrachoron of 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).

Representations
A prismatorhombated icositetrachoron has the following Coxeter diagrams:


 * x3x4o3x (full symmetry)
 * s3s4x3x (as runcicantic snub icositetrachoron)
 * ox4xx3xx3wx&#zx (D4 symmetry)
 * wxx3xxx3xwx *b3xxw&#zx (D4 symmetry)
 * xux4qoo3xxx3oqQ&#zx (BC4 symmetry, dual ico)

Related polychora
The segmentochoron truncated octahedron atop great rhombicuboctahedron can be obtained as a cap of the prismatorhombated icositetrachoron. If eight of these caps are removed the result is the great disprismatotesseractihexadecachoron.