Snub tetracontoctachoron

The omnisnub icositetrachoron, or sni, also commonly called the omnisnub 24-cell, is a convex isogonal polychoron that consists of 48 snub cubes, 192 triangular antiprisms and 576 phyllic disphenoids obtained through the process of alternating the great prismatotetracontoctachoron. However, it cannot be made uniform.

Vertex coordinates
Vertex coordinates for an omnisnub icositetrachoron, created from the vertices of a great prismatotetracontoctachoron of edge length 1, are given by all even permutations with an even number of sign changes, plus all odd permutations with an odd amount of sign changes, of:
 * (±(5+3$\sqrt{2}$)/2, ±(1+2$\sqrt{2}$)/2, ±(1+$\sqrt{2}$)/2, ±1/2)
 * (±3(1+$\sqrt{2}$)/2, ±(3+2$\sqrt{2}$)/2, ±(3+$\sqrt{2}$)/2, ±1/2)
 * (±(4+3$\sqrt{2}$)/2, ±(1+$\sqrt{2}$), ±(2+$\sqrt{2}$)/2, ±1)