Snub tetracontoctachoron

The snub tetracontoctachoron, or snoc, also commonly called the omnisnub icositetrachoron or 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 a snub tetracontoctachoron, 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:
 * (±1/2, ±(1+$\sqrt{2}$)/2, ±(1+2$\sqrt{2}$)/2, ±(5+3$\sqrt{2}$)/2),
 * (±1/2, ±(3+$\sqrt{2}$)/2, ±(3+2$\sqrt{2}$)/2, ±(3+3$\sqrt{2}$)/2),
 * (±1, ±(2+$\sqrt{2}$)/2, ±(1+$\sqrt{2}$), ±(4+3$\sqrt{2}$)/2).

An alternate set of coordinates, assuming that the edge length differences are minimized, centered at the origin, 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:
 * (±$\sqrt{4-2√2}$/4, ±$\sqrt{4+2√2}$/4, ±(2+$\sqrt{4+2√2}$)/4), ±(2+2$\sqrt{2}$+$\sqrt{20+14√2}$)/4),
 * (±$\sqrt{2}$/4, ±($\sqrt{2}$+$\sqrt{8+4√2}$)/4, ±(2+$\sqrt{2}$+$\sqrt{8+4√2}$)/4, ±(2+$\sqrt{2}$+$\sqrt{16+8√2}$)/4),
 * (±($\sqrt{2}$+$\sqrt{4-2√2}$)/4, ±($\sqrt{2}$+$\sqrt{4+2√2}$)/4, ±(2+$\sqrt{2}$+$\sqrt{4+2√2}$)/4, ±(2+$\sqrt{2}$+$\sqrt{20+14√2}$)/4).