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 omnisnub hecatonicosachoron, although it cannot be made uniform.

Its dual is the largest possible 4D fair die, with 14,400 isochoral faces.

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).