Stellated tetracontoctachoron

The stellated tetracontoctachoron is a regular compound polychoron. It is a compound of two icositetrachora in dual orientation.

Vertex coordinates
The vertices of a stellated tetracontoctachoron of edge length 1, centered at the origin, are given by all permutations of:
 * $$\left(±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0,\,0\right).$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac12,\,±\frac12\right),$$
 * $$\left(±1,\,0,\,0,\,0\right).$$