Small prismatotetracontoctachoron

The small prismatotetracontoctachoron, or spic, also commonly called the runcinated 24-cell, is a convex uniform polychoron that consists of 48 regular octahedra and 192 triangular prisms. 2 octahedra and 8 triangular prisms join at each vertex. It is the result of expanding the cells of an icositetrachoron outwards.

The small prismatotetracontoctachoron contains the vertices of an 8-8 duoprism, truncated cube prism and the triangular double prismantiprismoid.

Vertex coordinates
The vertices of a small prismatotetracontoctachoron of edge length 1 are all permutations of:


 * (±(2+$\sqrt{2}$)/2, ±$\sqrt{2+√2}$/2, 0, 0)
 * (±(1+$\sqrt{2}$)/2, ±(1+$\sqrt{2}$)/2, ±1/2, ±1/2).

The second set of vertices are identical to the vertices of an inscribed small rhombated tesseract.