Great rhombated hecatonicosachoric prism

The great rhombated hecatonicosachoric prism or grahip is a prismatic uniform polyteron that consists of 2 great rhombated hecatonicosachora, 120 great rhombicosidodecahedral prisms, 600 truncated tetrahedral prisms, and 1200 triangular-square duoprisms. 1 great rhombated hecatonicosachoron, 2 great rhombicosidodecahedral prisms, 1 truncated tetrahedral prism, and 1 triangular-square duoprism join at each vertex. As the name suggests, it is a prism based on the great rhombated hecatonicosachoron, which also makes it a convex segmentoteron.

Vertex coordinates
The vertices of a great rhombated hecatonicosachoric prism of edge length 1 are given by all permutations of the first four coordinates of: plus all even permutations of the first four coordinates of:
 * $$\left(±\frac12,\,±\frac12,\,±\frac{3+2\sqrt5}{2},\,±5\frac{2+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{5+3\sqrt5}{4},\,±3\frac{3+\sqrt5}{4},\,±\frac{13+7\sqrt5}{4},\,±\frac{13+7\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{7+3\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac{11+7\sqrt5}{4},\,±\frac{15+7\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{19+7\sqrt5}{4},\,±\frac{13+7\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(0,\,±\frac12,\,±3\frac{7+3\sqrt5}{4},\,±\frac{7+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(0,\,±\frac{3+\sqrt5}{4},\,±\frac{9+4\sqrt5}{2},\,±\frac{11+7\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(0,\,±\frac{3+\sqrt5}{4},\,±\frac{11+4\sqrt5}{2},\,±\frac{9+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{2},\,±(5+2\sqrt5),\,±\frac{5+3\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{13+5\sqrt5}{4},\,±\frac{7+3\sqrt5}{2},\,±5\frac{3+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±1,\,±\frac{17+7\sqrt5}{4},\,±\frac{15+7\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{5+\sqrt5}{4},\,±2(2+\sqrt5),\,±\frac{13+7\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt5}{2},\,±\frac{11+4\sqrt5}{2},\,±\frac{5+2\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt5}{2},\,±5\frac{2+\sqrt5}{2},\,±\frac{4+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±3\frac{1+\sqrt5}{4},\,±(5+2\sqrt5),\,±\frac{11+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{7+3\sqrt5}{4},\,±2(2+\sqrt5),\,±5\frac{3+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±1,\,±\frac{3+\sqrt5}{4},\,±5\frac{2+\sqrt5}{2},\,±\frac{7+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±1,\,±\frac{2+\sqrt5}{2},\,±3\frac{7+3\sqrt5}{4},\,±3\frac{3+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±1,\,±\frac{3+\sqrt5}{2},\,±2(2+\sqrt5),\,±\frac{7+3\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±1,\,±\frac{5+3\sqrt5}{4},\,±\frac{9+4\sqrt5}{2},\,±\frac{13+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{11+5\sqrt5}{4},\,±\frac{13+7\sqrt5}{4},\,±5\frac{3+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±3\frac{1+\sqrt5}{4},\,±5\frac{2+\sqrt5}{2},\,±\frac{3+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±3\frac{3+\sqrt5}{4},\,±\frac{17+7\sqrt5}{4},\,±5\frac{3+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{5+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±5\frac{2+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{5+2\sqrt5}{2},\,±\frac{15+7\sqrt5}{4},\,±5\frac{3+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±3\frac{1+\sqrt5}{4},\,±3\frac{7+3\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±\frac{4+\sqrt5}{2},\,±\frac{17+7\sqrt5}{4},\,±\frac{7+3\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac{19+7\sqrt5}{4},\,±\frac{13+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac{11+5\sqrt5}{4},\,±\frac{11+7\sqrt5}{4},\,±\frac{7+3\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac{5+3\sqrt5}{2},\,±\frac{13+7\sqrt5}{4},\,±\frac{13+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±3\frac{1+\sqrt5}{4},\,±\frac{9+5\sqrt5}{4},\,±\frac{15+7\sqrt5}{4},\,±\frac{13+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±3\frac{1+\sqrt5}{4},\,±\frac{5+2\sqrt5}{2},\,±\frac{13+7\sqrt5}{4},\,±\frac{7+3\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{2},\,±\frac{5+3\sqrt5}{4},\,±\frac{11+4\sqrt5}{2},\,±\frac{7+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{2},\,±\frac{4+\sqrt5}{2},\,±\frac{15+7\sqrt5}{4},\,±\frac{13+7\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{2},\,±\frac{3+2\sqrt5}{2},\,±\frac{19+7\sqrt5}{4},\,±\frac{11+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{5+3\sqrt5}{4},\,±\frac{7+5\sqrt5}{4},\,±\frac{17+7\sqrt5}{4},\,±\frac{11+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{4+\sqrt5}{2},\,±\frac{7+3\sqrt5}{4},\,±(5+2\sqrt5),\,±3\frac{3+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{4+\sqrt5}{2},\,±\frac{3+2\sqrt5}{2},\,±\frac{9+4\sqrt5}{2},\,±\frac{5+2\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{7+3\sqrt5}{4},\,±\frac{3+2\sqrt5}{2},\,±\frac{17+7\sqrt5}{4},\,±\frac{5+3\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{7+3\sqrt5}{4},\,±\frac{7+5\sqrt5}{4},\,±2(2+\sqrt5),\,±\frac{5+2\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{3+2\sqrt5}{2},\,±3\frac{3+\sqrt5}{4},\,±\frac{9+5\sqrt5}{4},\,±2(2+\sqrt5),\,±\frac12\right).$$