Rectified small prismatotetracontoctachoron

The rectified small prismatotetracontoctachoron or respic is a convex isogonal polychoron that consists of 48 cuboctahedra, 192 rectified triangular prisms and 144 square antiprisms. 1 cuboctahedron, 3 rectified triangular prisms, and 2 square antiprisms join at each vertex. It can be formed by rectifying the small prismatotetracontoctachoron.

It can also be formed as the convex hull of 2 oppositely oriented semi-uniform variants of the small rhombated icositetrachoron, where the edges of the cuboctahedra are half the length of the other edges.

The ratio between the longest and shortest edges is 1:$$\sqrt2$$ ≈ 1:1.41421.

Vertex coordinates
The vertices of a rectified small prismatotetracontoctachoron with triangles of edge length 1, centered at the origin, are given by:


 * $$\left(0,\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,±(2+\sqrt2)\right),$$
 * $$\left(±1,\,±\frac{2+\sqrt2}{2},\,±\frac{2+\sqrt2}{2},\,±(1+\sqrt2)\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{1+2\sqrt2}{2},\,±\frac{3+2\sqrt2}{2}\right),$$
 * $$\left(0,\,±1,\,±(1+\sqrt2),\,±(1+\sqrt2)\right).$$