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. Together with its dual, it is the first in an infinite family of cuboctahedral swirlchora.

The small prismatotetracontoctachoron contains the vertices of an octagonal duoprism, small rhombated tesseract, truncated cubic 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.