Small stellated tetracontoctachoron

The small stellated tetracontoctachoron or sistic is a regular compound polychoron. It is a compound of six hexadecachora, and of two stellated icositetrachora in opposite orientations.

Vertex coordinates
The vertices of a small stellated tetracontoctachoron of edge length 1, centered at the origin, are given by all permutations of:
 * $$\left(±\frac12,\,±\frac12,\,0,\,0\right).$$
 * $$\left(±\frac{\sqrt2}{4},\,±\frac{\sqrt2}{4},\,±\frac{\sqrt2}{4},\,±\frac{\sqrt2}{4}\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,0,\,0,\,0\right).$$