Great tetracontoctachoron

The great tetracontoctachoron, or gic, is a nonconvex noble uniform polychoron that consists of 48 quasitruncated hexahedra as cells. Four cells join at each vertex. It can be considered to be the biquasitruncation of the icositetrachoron and is conjugate to the convex tetracontoctachoron.

The density of the great tetracontachoron is 73. The vertex-angle is 1/288.

Vertex coordinates
Coordinates for the vertices of a great tetracontoctachoron of edge length 1 are all permutations of:


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