Small rhombated icositetrachoron

The small rhombated icositetrachoron, or srico, also commonly called the cantellated 24-cell, is a convex uniform polychoron that consists of 96 triangular prisms, 24 cuboctahedra and 24 small rhombicuboctahedra. 2 triangular prisms, 1 cuboctahedron, and 2 small rhombicuboctahedra join at each vertex. As one of its names suggests, it can be obtained by cantellating the icositetrachoron.

Vertex coordinates
The vertices of a small rhombated icositetrachoron of edge length 1 are given by all permutations of:
 * (±(1+$\sqrt{2}$), ±$\sqrt{4+2√2}$/2, ±$\sqrt{2}$/2, 0),
 * (±(1+2$\sqrt{6}$)/2, ±(1+$\sqrt{2}$)/2, ±(1+$\sqrt{2}$)/2, ±1/2).

The second set of vertices are identical to those of an inscribed prismatorhombated hexadecachoron.

The cantellation of the dual icositetrachoron has vertex coordinates given by:
 * (±(2+$\sqrt{2}$)/2, ±(2+$\sqrt{2}$)/2, ±1, 0),
 * (±(3+$\sqrt{2}$)/2, ±(1+$\sqrt{2}$)/2, ±1/2, ±1/2).

Representations
A small rhombated icositetrachoron has the following Coxeter diagrams:


 * x3o4x3o (full symmetry)
 * s3s4x3o (half symmetry, as cantic snub icositetrachoron)
 * oxxowqwoxxo4xxxxoooxxxx3ooxwxwxwxoo&#xt (BC3 axial, cuboctahedron-first)
 * xoxoxuxoxox4oqowxxxwoqo3xxwoqoqowxx&#xt (BC3 axial, small rhombicuboctahedron-first)
 * ox4xx3oo3wx&#zx (BC4 symmetry)
 * xo4oq3xx3qo&#zx (BC4 symmetry, dual ico positioning)
 * wxx3ooo3xwx *b3xxw&#zx (D4 symmetry)

Related polychora
The segmentochoron cuboctahedron atop truncated cube can be obtained as a cap of the small rhombated icositetrachoron. If 8 of these caps are removed, the result is the prismatorhombated hexadecachoron, with the small rhombicuboctahedral cells all cut down to their central octagonal prism segments only.