Truncated icositetrachoron

The truncated icositetrachoron, or tico, also commonly called the truncated 24-cell, is a convex uniform polychoron that consists of 24 cubes and 24 truncated octahedra. 1 cube and 3 truncated octahedra join at each vertex. As the name suggests, it can be obtained as the truncation of an icositetrachoron.

It is also the cantitruncated hexadecachoron, and the omnitruncated demitesseract.

Vertex coordinates
The vertices of a truncated icositetrachoron of edge length 1 are given by all permutations of:


 * (±3$\sqrt{2}$/2, ±$\sqrt{3}$, ±$\sqrt{7}$/2, 0).

The vertices of the truncation of the dual icositetrachoron can be given by all permutations of:


 * (±5/2, ±1/2, ±1/2, ±1/2),
 * (±3/2, ±3/2, ±3/2, ±1/2),
 * (±2, ±1, ±1, ±1).

Representations
A truncated icositetrachoron has the following Coxeter diagrams:


 * x3x4o3o (full symmetry)
 * o4x3x3x (BC4 symmetry, great rhombated hexadecachoron)
 * x3x3x *b3x (D4 symmetry, omnitruncated demitesseract)
 * s4x3x3x (as snub)
 * oooqooo3xxuxuxx3xuxxxux&#xt (BC3 axial, truncated octahedron-first)
 * xux3qoo3ooo3oqQ&#zx (D4 symmetry, truncated dual ico)