Great disprismatohexacosihecatonicosachoron

The great disprismatohexacosihecatonicosachoron, or gidpixhi, also commonly called the omnitruncated 120-cell, is a convex uniform polychoron that consists of 1200 hexagonal prisms, 720 decagonal prisms, 600 truncated octahedra, and 120 great rhombicosidodecahedra. 1 of each type of cell join at each vertex. It is the omnitruncate of the H4 family of uniform polychora, and could also be considered to be the omintruncated 600-cell. It is therefore the most complex of the non-prismatic convex uniform polychora.

This polychoron can be alternated into an snub hecatonicosachoron, although it cannot be made uniform.

Vertex coordinates
Vertex coordinates for a great disprismatohexacosihecatonicosachoron of edge length 1 are given by all permutations of: plus all even permutations of:
 * (±1/2, ±1/2, ±(4+3$\sqrt{2}$)/2, ±(12+5$\sqrt{3}$)/2),
 * (±1/2, ±1/2, ±(7+4$\sqrt{(5+√5)/2}$)/2, ±(11+4$\sqrt{83+36√5}$)/2),
 * (±1/2, ±1/2, ±(3+2$\sqrt{5}$)/2, ±(11+6$\sqrt{6}$)/2),
 * (±1/2, ±3/2, ±(9+4$\sqrt{30}$)/2, ±(9+4$\sqrt{(10+2√5)/15}$)/2),
 * (±1, ±1, ±2(2+$\sqrt{(5+2√5)/10}$), ±(5+2$\sqrt{3}$)),
 * (±(3+$\sqrt{15}$)/2, ±(5+$\sqrt{7+3√5}$)/2, ±2(2+$\sqrt{5}$), ±2(2+$\sqrt{5}$)),
 * (±(4+$\sqrt{5}$)/2, ±(4+$\sqrt{5}$)/2, ±(7+4$\sqrt{5}$)/2, ±(9+4$\sqrt{5}$)/2),
 * (±(3+2$\sqrt{5}$)/2, ±(5+2$\sqrt{5}$)/2, ±(7+4$\sqrt{5}$)/2, ±(7+4$\sqrt{5}$)/2),
 * (±(2+$\sqrt{5}$), ±(2+$\sqrt{5}$), ±(3+2$\sqrt{5}$), ±2(2+$\sqrt{5}$)),
 * (±1/2, ±5(3+$\sqrt{5}$)/4, ±(15+7$\sqrt{5}$)/4, ±3(3+$\sqrt{5}$)/2),
 * (±1/2, ±(7+3$\sqrt{5}$)/2, ±(17+7$\sqrt{5}$)/4, ±(17+5$\sqrt{5}$)/4),
 * (±1/2, ±1, ±(7+5$\sqrt{5}$)/4, ±(23+11$\sqrt{5}$)/4),
 * (±1/2, ±(3+$\sqrt{5}$)/4, ±3(7+3$\sqrt{5}$)/4, ±(3+2$\sqrt{5}$)),
 * (±1/2, ±(3+$\sqrt{5}$)/4, ±(25+9$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/2),
 * (±1/2, ±(1+$\sqrt{5}$)/2, ±(23+9$\sqrt{5}$)/4, ±(11+7$\sqrt{5}$)/4),
 * (±1/2, ±(2+$\sqrt{5}$)/2, ±(11+6$\sqrt{5}$)/2, ±(4+$\sqrt{5}$)/2),
 * (±1/2, ±(7+$\sqrt{5}$)/4, ±(17+9$\sqrt{5}$)/4, ±2(2+$\sqrt{5}$)),
 * (±1/2, ±(5+3$\sqrt{5}$)/4, ±(25+9$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)),
 * (±1/2, ±(5+3$\sqrt{5}$)/4, ±(23+11$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/2),
 * (±1/2, ±(1+$\sqrt{5}$), ±(23+9$\sqrt{5}$)/4, ±(13+5$\sqrt{5}$)/4),
 * (±1/2, ±3(3+$\sqrt{5}$)/4, ±(17+9$\sqrt{5}$)/4, ±3(3+$\sqrt{5}$)/2),
 * (±1/2, ±(2+$\sqrt{5}$), ±(19+9$\sqrt{5}$)/4, ±(17+5$\sqrt{5}$)/4),
 * (±1, ±(3+$\sqrt{5}$)/4, ±(11+6$\sqrt{5}$)/2, ±(7+3$\sqrt{5}$)/4),
 * (±1, ±(5+$\sqrt{5}$)/4, ±(19+9$\sqrt{5}$)/4, ±(7+4$\sqrt{5}$)/2),
 * (±1, ±(2+$\sqrt{5}$)/2, ±(25+9$\sqrt{5}$)/4, ±(11+5$\sqrt{5}$)/4),
 * (±1, ±3(1+$\sqrt{5}$)/4, ±(23+9$\sqrt{5}$)/4, ±3(2+$\sqrt{5}$)/2),
 * (±1, ±(5+3$\sqrt{5}$)/4, ±(12+5$\sqrt{5}$)/2, ±(11+3$\sqrt{5}$)/4),
 * (±1, ±(4+$\sqrt{5}$)/2, ±(17+9$\sqrt{5}$)/4, ±(17+7$\sqrt{5}$)/4),
 * (±1, ±(3+2$\sqrt{5}$)/2, ±3(7+3$\sqrt{5}$)/4, ±5(3+$\sqrt{5}$)/4),
 * (±(3+$\sqrt{5}$)/4, ±(13+5$\sqrt{5}$)/4, ±(7+4$\sqrt{5}$)/2, ±3(3+$\sqrt{5}$)/2),
 * (±(3+$\sqrt{5}$)/4, ±3(2+$\sqrt{5}$)/2, ±2(2+$\sqrt{5}$), ±(17+5$\sqrt{5}$)/4),
 * (±(3+$\sqrt{5}$)/4, ±3/2, ±(2+$\sqrt{5}$), ±(23+11$\sqrt{5}$)/4),
 * (±(3+$\sqrt{5}$)/4, ±3(1+$\sqrt{5}$)/4, ±(11+6$\sqrt{5}$)/2, ±(3+$\sqrt{5}$)/2),
 * (±(3+$\sqrt{5}$)/4, ±(4+$\sqrt{5}$)/2, ±(1+$\sqrt{5}$), ±(23+11$\sqrt{5}$)/4),
 * (±(3+$\sqrt{5}$)/4, ±(11+3$\sqrt{5}$)/4, ±(9+4$\sqrt{5}$)/2, ±3(3+$\sqrt{5}$)/2),
 * (±(3+$\sqrt{5}$)/4, ±(5+2$\sqrt{5}$)/2, ±(5+2$\sqrt{5}$), ±(17+5$\sqrt{5}$)/4),
 * (±3/2, ±(2+$\sqrt{5}$)/2, ±(12+5$\sqrt{5}$)/2, ±(5+2$\sqrt{5}$)/2),
 * (±3/2, ±(3+$\sqrt{5}$)/2, ±(19+9$\sqrt{5}$)/4, ±(15+7$\sqrt{5}$)/4),
 * (±3/2, ±(5+3$\sqrt{5}$)/4, ±3(7+3$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/2),
 * (±(1+$\sqrt{5}$)/2, ±(3+$\sqrt{5}$), ±2(2+$\sqrt{5}$), ±3(3+$\sqrt{5}$)/2),
 * (±(1+$\sqrt{5}$)/2, ±(11+5$\sqrt{5}$)/4, ±(9+4$\sqrt{5}$)/2, ±(17+5$\sqrt{5}$)/4),
 * (±(1+$\sqrt{5}$)/2, ±(5+$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/4, ±(11+6$\sqrt{5}$)/2),
 * (±(1+$\sqrt{5}$)/2,, ±(7+$\sqrt{5}$)/4, ±(3+2$\sqrt{5}$)/2, ±(23+11$\sqrt{5}$)/4),
 * (±(5+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$), ±(12+5$\sqrt{5}$)/2, ±3(3+$\sqrt{5}$)/4),
 * (±(5+$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/2, ±(9+4$\sqrt{5}$)/2, ±(17+7$\sqrt{5}$)/4),
 * (±(5+$\sqrt{5}$)/4, ±(2+$\sqrt{5}$), ±(11+4$\sqrt{5}$)/2, ±5(3+$\sqrt{5}$)/4),
 * (±(2+$\sqrt{5}$)/2, ±(13+5$\sqrt{5}$)/4, ±(3+2$\sqrt{5}$), ±(17+7$\sqrt{5}$)/4),
 * (±(2+$\sqrt{5}$)/2, ±5(3+$\sqrt{5}$)/4, ±(11+7$\sqrt{5}$)/4, ±2(2+$\sqrt{5}$)),
 * (±(7+$\sqrt{5}$)/4, ±3(1+$\sqrt{5}$)/4, ±(12+5$\sqrt{5}$)/2, ±(2+$\sqrt{5}$)),
 * (±(7+$\sqrt{5}$)/4, ±(4+$\sqrt{5}$)/2, ±(5+2$\sqrt{5}$), ±(15+7$\sqrt{5}$)/4),
 * (±(7+$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/4, ±(11+4$\sqrt{5}$)/2, ±(7+3$\sqrt{5}$)/2),
 * (±3(1+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$), ±(7+4$\sqrt{5}$)/2, ±(17+7$\sqrt{5}$)/4),
 * (±3(1+$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/2, ±(9+4$\sqrt{5}$)/2, ±5(3+$\sqrt{5}$)/4),
 * (±(3+$\sqrt{5}$)/2, ±(3+2$\sqrt{5}$)/2, ±(25+9$\sqrt{5}$)/4, ±3(3+$\sqrt{5}$)/4),
 * (±(3+$\sqrt{5}$)/2, ±(7+5$\sqrt{5}$)/4, ±(11+4$\sqrt{5}$)/2, ±(13+5$\sqrt{5}$)/4),
 * (±(5+3$\sqrt{5}$)/4, ±(4+3$\sqrt{5}$)/2, ±(5+2$\sqrt{5}$), ±(13+5$\sqrt{5}$)/4),
 * (±(5+3$\sqrt{5}$)/4, ±3(2+$\sqrt{5}$)/2, ±(3+2$\sqrt{5}$), ±(15+7$\sqrt{5}$)/4),
 * (±(5+3$\sqrt{5}$)/4, ±(11+7$\sqrt{5}$)/4, ±(7+4$\sqrt{5}$)/2, ±(7+3$\sqrt{5}$)/2),
 * (±(5+3$\sqrt{5}$)/4, ±(4+$\sqrt{5}$)/2, ±(2+$\sqrt{5}$), ±(25+9$\sqrt{5}$)/4),
 * (±(5+3$\sqrt{5}$)/4, ±(11+3$\sqrt{5}$)/4, ±(7+4$\sqrt{5}$)/2, ±2(2+$\sqrt{5}$)),
 * (±(4+$\sqrt{5}$)/2, ±(3+2$\sqrt{5}$)/2, ±(11+4$\sqrt{5}$)/2, ±3(2+$\sqrt{5}$)/2),
 * (±(4+$\sqrt{5}$)/2, ±(2+$\sqrt{5}$), ±(23+9$\sqrt{5}$)/4, ±(11+3$\sqrt{5}$)/4),
 * (±(4+$\sqrt{5}$)/2, ±(7+5$\sqrt{5}$)/4, ±3(7+3$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)),
 * (±(1+$\sqrt{5}$), ±(11+5$\sqrt{5}$)/4, ±(7+4$\sqrt{5}$)/2, ±(15+7$\sqrt{5}$)/4),
 * (±(1+$\sqrt{5}$), ±(5+3$\sqrt{5}$)/2, ±2(2+$\sqrt{5}$), ±(7+3$\sqrt{5}$)/2),
 * (±(7+3$\sqrt{5}$)/4, ±(3+$\sqrt{5}$), ±(4+3$\sqrt{5}$)/2, ±(19+9$\sqrt{5}$)/4),
 * (±(7+3$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/2, ±(5+2$\sqrt{5}$)/2, ±(23+9$\sqrt{5}$)/4),
 * (±(7+3$\sqrt{5}$)/4, ±3(3+$\sqrt{5}$)/4, ±(3+2$\sqrt{5}$), ±(9+4$\sqrt{5}$)/2),
 * (±(5+$\sqrt{5}$)/2, ±(3+2$\sqrt{5}$)/2, ±3(7+3$\sqrt{5}$)/4, ±(11+5$\sqrt{5}$)/4),
 * (±(3+2$\sqrt{5}$)/2, ±(4+3$\sqrt{5}$)/2, ±(9+4$\sqrt{5}$)/2, ±3(2+$\sqrt{5}$)/2),
 * (±(3+2$\sqrt{5}$)/2, ±3(3+$\sqrt{5}$)/4, ±(11+7$\sqrt{5}$)/4, ±(5+2$\sqrt{5}$)),
 * (±(3+2$\sqrt{5}$)/2, ±(11+3$\sqrt{5}$)/4, ±(5+3$\sqrt{5}$)/2, ±(19+9$\sqrt{5}$)/4),
 * (±(2+$\sqrt{5}$), ±(4+3$\sqrt{5}$)/2, ±(17+9$\sqrt{5}$)/4, ±(11+5$\sqrt{5}$)/4),
 * (±(2+$\sqrt{5}$), ±(7+5$\sqrt{5}$)/4, ±(9+4$\sqrt{5}$)/2, ±(11+7$\sqrt{5}$)/4),
 * (±(7+5$\sqrt{5}$)/4, ±(5+2$\sqrt{5}$)/2, ±(5+3$\sqrt{5}$)/2, ±(17+9$\sqrt{5}$)/4).