Great disprismatohexacosihecatonicosachoric prism

The great disprismatohexacosihecatonicosachoric prism or gidpixhip is a prismatic uniform polyteron that consists of 2 great disprismatohexacosihecatonicosachora, 120 great rhombicosidodecahedral prisms, 600 truncated octahedral prisms, 720 square-decagonal duoprisms and 1200 square-hexagonal duoprisms. One of each type of facet join at each vertex. As the name suggests, it can be obtained as a prism based on the great disprismatohexacosihecatonicosachoron, which also makes it a convex segmentoteron.

This polyteron can be alternated into an omnisnub hecatonicosachoric antiprism, although it cannot be made uniform.

Vertex coordinates
Vertex coordinates for a great disprismatohexacosihecatonicosachoric 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:
 * $$\left(±\frac12,\,±\frac12,\,±\frac{4+3\sqrt5}{2},\,±\frac{12+5\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{7+4\sqrt5}{2},\,±\frac{11+4\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{3+2\sqrt5}{2},\,±\frac{11+6\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac32,\,±\frac{9+4\sqrt5}{2},\,±\frac{9+4\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±1,\,±1,\,±2(2+\sqrt5),\,±(5+2\sqrt5),\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{2},\,±\frac{5+\sqrt5}{2},\,±2(2+\sqrt5),\,±2(2+\sqrt5),\,±\frac12\right),$$
 * $$\left(±\frac{4+\sqrt5}{2},\,±\frac{4+\sqrt5}{2},\,±\frac{7+4\sqrt5}{2},\,±\frac{9+4\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{3+2\sqrt5}{2},\,±\frac{5+2\sqrt5}{2},\,±\frac{7+4\sqrt5}{2},\,±\frac{7+4\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±(2+\sqrt5),\,±(2+\sqrt5),\,±(3+2\sqrt5),\,±2(2+\sqrt5),\,±\frac12\right),$$
 * $$\left(±\frac12,\,±5\frac{3+\sqrt5}{4},\,±\frac{15+7\sqrt5}{4},\,±3\frac{3+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{7+3\sqrt5}{2},\,±\frac{17+7\sqrt5}{4},\,±\frac{17+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±1,\,±\frac{7+5\sqrt5}{4},\,±\frac{23+11\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±3\frac{7+3\sqrt5}{4},\,±(3+2\sqrt5),\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±\frac{25+9\sqrt5}{4},\,±\frac{5+3\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{2},\,±\frac{23+9\sqrt5}{4},\,±\frac{11+7\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt5}{2},\,±\frac{11+6\sqrt5}{2},\,±\frac{4+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\, ±\frac{7+\sqrt5}{4},\,±\frac{17+9\sqrt5}{4},\,±2(2+\sqrt5),\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{5+3\sqrt5}{4},\,±\frac{25+9\sqrt5}{4},\,±(3+\sqrt5),\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{5+3\sqrt5}{4},\,±\frac{23+11\sqrt5}{4},\,±\frac{5+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±(1+\sqrt5),\,±\frac{23+9\sqrt5}{4},\,±\frac{13+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±3\frac{3+\sqrt5}{4},\,±\frac{17+9\sqrt5}{4},\,±3\frac{3+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±(2+\sqrt5),\,±\frac{19+9\sqrt5}{4},\,±\frac{17+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±1,\,±\frac{3+\sqrt5}{4},\,±\frac{11+6\sqrt5}{2},\,±\frac{7+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±1,\,±\frac{5+\sqrt5}{4},\,±\frac{19+9\sqrt5}{4},\,±\frac{7+4\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±1,\,±\frac{2+\sqrt5}{2},\,±\frac{25+9\sqrt5}{4},\,±\frac{11+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±1,\,±3\frac{1+\sqrt5}{4},\,±\frac{23+9\sqrt5}{4},\,±3\frac{2+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±1,\,±\frac{5+3\sqrt5}{4},\,±\frac{12+5\sqrt5}{2},\,±\frac{11+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±1,\,±\frac{4+\sqrt5}{2},\,±\frac{17+9\sqrt5}{4},\,±\frac{17+7\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±1,\,±\frac{3+2\sqrt5}{2},\,±3\frac{7+3\sqrt5}{4},\,±5\frac{3+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{13+5\sqrt5}{4},\,±\frac{7+4\sqrt5}{2},\,±3\frac{3+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±3\frac{2+\sqrt5}{2},\,±2(2+\sqrt5),\,±\frac{17+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac32,\,±(2+\sqrt5),\,±\frac{23+11\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±3\frac{1+\sqrt5}{4},\,±\frac{11+6\sqrt5}{2},\,±\frac{3+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{4+\sqrt5}{2},\,±(1+\sqrt5),\,±\frac{23+11\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{11+3\sqrt5}{4},\,±\frac{9+4\sqrt5}{2},\,±3\frac{3+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{5+2\sqrt5}{2},\,±(5+2\sqrt5),\,±\frac{17+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac32,\,±\frac{2+\sqrt5}{2},\,±\frac{12+5\sqrt5}{2},\,±\frac{5+2\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac32,\,±\frac{3+\sqrt5}{2},\,±\frac{19+9\sqrt5}{4},\,±\frac{15+7\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac32,\,±\frac{5+3\sqrt5}{4},\,±3\frac{7+3\sqrt5}{4},\,±\frac{7+3\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±(3+\sqrt5),\,±2(2+\sqrt5),\,±3\frac{3+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{11+5\sqrt5}{4},\,±\frac{9+4\sqrt5}{2},\,±\frac{17+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{5+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac{11+6\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},,\,±\frac{7+\sqrt5}{4},\,±\frac{3+2\sqrt5}{2},\,±\frac{23+11\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±(1+\sqrt5),\,±\frac{12+5\sqrt5}{2},\,±3\frac{3+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±\frac{5+\sqrt5}{2},\,±\frac{9+4\sqrt5}{2},\,±\frac{17+7\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±(2+\sqrt5),\,±\frac{11+4\sqrt5}{2},\,±5\frac{3+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac{13+5\sqrt5}{4},\,±(3+2\sqrt5),\,±\frac{17+7\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±5\frac{3+\sqrt5}{4},\,±\frac{11+7\sqrt5}{4},\,±2(2+\sqrt5),\,±\frac12\right),$$
 * $$\left(±\frac{7+\sqrt5}{4},\,±3\frac{1+\sqrt5}{4},\,±\frac{12+5\sqrt5}{2},\,±(2+\sqrt5),\,±\frac12\right),$$
 * $$\left(±\frac{7+\sqrt5}{4},\,±\frac{4+\sqrt5}{2},\,±(5+2\sqrt5),\,±\frac{15+7\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{7+\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac{11+4\sqrt5}{2},\,±\frac{7+3\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±3\frac{1+\sqrt5}{4},\,±(3+\sqrt5),\,±\frac{7+4\sqrt5}{2},\,±\frac{17+7\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±3\frac{1+\sqrt5}{4},\,±\frac{5+3\sqrt5}{2},\,±\frac{9+4\sqrt5}{2},\,±5\frac{3+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{2},\,±\frac{3+2\sqrt5}{2},\,±\frac{25+9\sqrt5}{4},\,±3\frac{3+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{2},\,±\frac{7+5\sqrt5}{4},\,±\frac{11+4\sqrt5}{2},\,±\frac{13+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{5+3\sqrt5}{4},\,±\frac{4+3\sqrt5}{2},\,±(5+2\sqrt5),\,±\frac{13+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{5+3\sqrt5}{4},\,±3\frac{2+\sqrt5}{2},\,±(3+2\sqrt5),\,±\frac{15+7\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{5+3\sqrt5}{4},\,±\frac{11+7\sqrt5}{4},\,±\frac{7+4\sqrt5}{2},\,±\frac{7+3\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{5+3\sqrt5}{4},\,±\frac{4+\sqrt5}{2},\,±(2+\sqrt5),\,±\frac{25+9\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{5+3\sqrt5}{4},\,±\frac{11+3\sqrt5}{4},\,±\frac{7+4\sqrt5}{2},\,±2(2+\sqrt5),\,±\frac12\right),$$
 * $$\left(±\frac{4+\sqrt5}{2},\,±\frac{3+2\sqrt5}{2},\,±\frac{11+4\sqrt5}{2},\,±3\frac{2+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{4+\sqrt5}{2},\,±(2+\sqrt5),\,±\frac{23+9\sqrt5}{4},\,±\frac{11+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{4+\sqrt5}{2},\,±\frac{7+5\sqrt5}{4},\,±3\frac{7+3\sqrt5}{4},\,±(3+\sqrt5),\,±\frac12\right),$$
 * $$\left(±(1+\sqrt5),\,±\frac{11+5\sqrt5}{4},\,±\frac{7+4\sqrt5}{2},\,±\frac{15+7\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±(1+\sqrt5),\,±\frac{5+3\sqrt5}{2},\,±2(2+\sqrt5),\,±\frac{7+3\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{7+3\sqrt5}{4},\,±(3+\sqrt5),\,±\frac{4+3\sqrt5}{2},\,±\frac{19+9\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{7+3\sqrt5}{4},\,±\frac{5+\sqrt5}{2},\,±\frac{5+2\sqrt5}{2},\,±\frac{23+9\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{7+3\sqrt5}{4},\,±3\frac{3+\sqrt5}{4},\,±(3+2\sqrt5),\,±\frac{9+4\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{5+\sqrt5}{2},\,±\frac{3+2\sqrt5}{2},\,±3\frac{7+3\sqrt5}{4},\,±\frac{11+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{3+2\sqrt5}{2},\,±\frac{4+3\sqrt5}{2},\,±\frac{9+4\sqrt5}{2},\,±3\frac{2+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{3+2\sqrt5}{2},\,±3\frac{3+\sqrt5}{4},\,±\frac{11+7\sqrt5}{4},\,±(5+2\sqrt5),\,±\frac12\right),$$
 * $$\left(±\frac{3+2\sqrt5}{2},\,±\frac{11+3\sqrt5}{4},\,±\frac{5+3\sqrt5}{2},\,±\frac{19+9\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±(2+\sqrt5),\,±\frac{4+3\sqrt5}{2},\,±\frac{17+9\sqrt5}{4},\,±\frac{11+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±(2+\sqrt5),\,±\frac{7+5\sqrt5}{4},\,±\frac{9+4\sqrt5}{2},\,±\frac{11+7\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{7+5\sqrt5}{4},\,±\frac{5+2\sqrt5}{2},\,±\frac{5+3\sqrt5}{2},\,±\frac{17+9\sqrt5}{4},\,±\frac12\right).$$