Great stellated tetracontoctachoron

The great stellated tetracontoctachoron or gistic is a regular compound polychoron. It is a compound of six tesseracts. It has 48 cubes as cells, with 8 cells joining at each vertex. It can also be seen as a compound of two great icositetrachora in opposite orientations, formed by replacing each icositetrachoron in the stellated tetracontoctachoron with a great icositetrachoron containing the same vertices and edges.

Like the great icositetrachoron, this compound has fissary vertices, with two components meeting per vertex.

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