Great quasidisprismatodishecatonicosachoron

Great quasidisprismatodishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Goquidipdy
Coxeter diagram	x5/3x5x3x ()
Elements
Cells	1200 hexagonal prisms, 720 decagrammic prisms, 120 quasitruncated dodecadodecahedra, 120 great rhombicosidodecahedra
Faces	3600+3600+3600 squares, 2400 hexagons, 1440 decagons, 1440 decagrams
Edges	7200+7200+7200+7200
Vertices	14400
Vertex figure	Irregular tetrahedron, edge lengths √2 (3), √3 (1), √(5+√5)/2 (1), and √(5–√5)/2 (1)
Measures (edge length 1)
Circumradius	${\sqrt {23+9{\sqrt {5}}}}\approx 6.56693$
Hypervolume	$525\left(37+16{\sqrt {5}}\right)\approx 38207.9710$
Dichoral angles	Stiddip–4–hip: $\arccos \left(-{\sqrt {\frac {10+2{\sqrt {5}}}{15}}}\right)\approx 169.18768^{\circ }$
	Quitdid–10/3–stiddip: 162°
	Quitdid–4–hip: $\arccos \left(-{\frac {{\sqrt {3}}+{\sqrt {15}}}{6}}\right)\approx 159.09484^{\circ }$
	Grid–10–quitdid: 36°
	Grid–4–stiddip: $\arccos \left({\sqrt {\frac {5+{\sqrt {5}}}{10}}}\right)\approx 31.71747^{\circ }$
	Grid–6–hip: 30°
Number of external pieces	21360
Level of complexity	113
Related polytopes
Army	Semi-uniform Gidpixhi, edge lengths ${\frac {3-{\sqrt {5}}}{2}}$ (decagons), ${\frac {{\sqrt {5}}-1}{2}}$ (remaining edges of great rhombicosidodecahedra), 1 (sides of decagonal prisms)
Regiment	Goquidipdy
Conjugate	Grand quasidisprismatodishecatonicosachoron
Convex core	Hecatonicosachoron
Abstract & topological properties
Flag count	345600
Euler characteristic	–480
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The great quasidisprismatodishecatonicosachoron, or goquidipdy, is a nonconvex uniform polychoron that consists of 1200 hexagonal prisms, 720 decagrammic prisms, 120 quasitruncated dodecadodecahedra, and 120 great rhombicosidodecahedra. 1 of each type of cell join at each vertex. It is the quasiomnitruncate of the faceted hexacosichoron and the small stellated hecatonicosachoron.

Cross-sections

Vertex coordinates

Vertex coordinates for a great quasidisprismatodishecatonicosachoron of edge length 1 are given by all permutations of:

• $\left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {3}{2}},\,\pm 3{\frac {2+{\sqrt {5}}}{2}}\right),$
• $\left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {4+{\sqrt {5}}}{2}},\,\pm {\frac {7+2{\sqrt {5}}}{2}}\right),$
• $\left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {3+2{\sqrt {5}}}{2}},\,\pm {\frac {4+3{\sqrt {5}}}{2}}\right),$
• $\left(\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm 5{\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {9+5{\sqrt {5}}}{4}}\right),$
• $\left(\pm 1,\,\pm 1,\,\pm {\frac {3+{\sqrt {5}}}{2}},\,\pm {\frac {5+3{\sqrt {5}}}{2}}\right),$
• $\left(\pm {\frac {\sqrt {5}}{2}},\,\pm {\frac {\sqrt {5}}{2}},\,\pm {\frac {1}{2}},\,\pm 3{\frac {2+{\sqrt {5}}}{2}}\right),$
• $\left(\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm 3{\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {13+3{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {1+{\sqrt {5}}}{2}},\,\pm {\frac {1+{\sqrt {5}}}{2}},\,\pm (1+{\sqrt {5}}),\,\pm (3+{\sqrt {5}})\right),$
• $\left(\pm {\frac {5+{\sqrt {5}}}{4}},\,\pm {\frac {5+{\sqrt {5}}}{4}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {13+5{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {\sqrt {5}}{2}},\,\pm {\frac {7+2{\sqrt {5}}}{2}}\right),$
• $\left(\pm {\frac {7+{\sqrt {5}}}{4}},\,\pm {\frac {7+{\sqrt {5}}}{4}},\,\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {11+5{\sqrt {5}}}{4}}\right),$
• $\left(\pm 3{\frac {1+{\sqrt {5}}}{4}},\,\pm 3{\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {7+3{\sqrt {5}}}{4}},\,\pm {\frac {11+3{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {5+3{\sqrt {5}}}{4}},\,\pm {\frac {5+3{\sqrt {5}}}{4}},\,\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {13+3{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {5+3{\sqrt {5}}}{4}},\,\pm {\frac {5+3{\sqrt {5}}}{4}},\,\pm {\frac {7+{\sqrt {5}}}{4}},\,\pm {\frac {7+5{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {4+{\sqrt {5}}}{2}},\,\pm {\frac {4+{\sqrt {5}}}{2}},\,\pm {\frac {\sqrt {5}}{2}},\,\pm {\frac {5+2{\sqrt {5}}}{2}}\right),$
• $\left(\pm {\frac {7+3{\sqrt {5}}}{4}},\,\pm {\frac {7+3{\sqrt {5}}}{4}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {11+3{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {7+3{\sqrt {5}}}{4}},\,\pm {\frac {7+3{\sqrt {5}}}{4}},\,\pm {\frac {5+{\sqrt {5}}}{4}},\,\pm 5{\frac {1+{\sqrt {5}}}{4}}\right),$
• $\left(\pm 3{\frac {3+{\sqrt {5}}}{4}},\,\pm 3{\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {1+3{\sqrt {5}}}{4}},\,\pm {\frac {5+3{\sqrt {5}}}{4}}\right),$
• $\left(\pm (2+{\sqrt {5}}),\,\pm (2+{\sqrt {5}}),\,\pm {\frac {3+{\sqrt {5}}}{2}},\,\pm {\frac {{\sqrt {5}}-1}{2}}\right),$
• $\left(\pm {\frac {11+3{\sqrt {5}}}{4}},\,\pm {\frac {11+3{\sqrt {5}}}{4}},\,\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {5+{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {7+5{\sqrt {5}}}{4}},\,\pm {\frac {7+5{\sqrt {5}}}{4}},\,\pm {\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {3+{\sqrt {5}}}{4}}\right),$

plus all even permutations of:

• $\left(\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {{\sqrt {5}}-1}{4}},\,\pm 3{\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {1+{\sqrt {5}}}{2}}\right),$
• $\left(\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}},\,\pm {\frac {5+3{\sqrt {5}}}{2}},\,\pm {\frac {5+3{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}},\,\pm (3+{\sqrt {5}}),\,\pm 3{\frac {3+{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {13+5{\sqrt {5}}}{4}},\,\pm 3{\frac {1+{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm 1,\,\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm 3{\frac {2+{\sqrt {5}}}{2}}\right),$
• $\left(\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm 3{\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {7+3{\sqrt {5}}}{4}},\,\pm {\frac {9+5{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {2+{\sqrt {5}}}{2}},\,\pm (2+{\sqrt {5}}),\,\pm {\frac {7+5{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {4+{\sqrt {5}}}{2}},\,\pm (2+{\sqrt {5}}),\,\pm 3{\frac {3+{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {{\sqrt {5}}-1}{4}},\,\pm 1,\,\pm {\frac {5+2{\sqrt {5}}}{2}},\,\pm {\frac {11+3{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {5+{\sqrt {5}}}{4}},\,\pm {\frac {3+{\sqrt {5}}}{2}},\,\pm {\frac {7+2{\sqrt {5}}}{2}}\right),$
• $\left(\pm {\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {1+3{\sqrt {5}}}{4}},\,\pm {\frac {5+3{\sqrt {5}}}{4}},\,\pm {\frac {11+5{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {1}{2}},\,\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {7+3{\sqrt {5}}}{4}},\,\pm {\frac {11+5{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {13+3{\sqrt {5}}}{4}},\,\pm (2+{\sqrt {5}})\right),$
• $\left(\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {13+5{\sqrt {5}}}{4}},\,\pm {\frac {7+{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {5}}}{2}},\,\pm {\frac {11+3{\sqrt {5}}}{4}},\,\pm {\frac {7+5{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {5}}}{2}},\,\pm {\frac {13+5{\sqrt {5}}}{4}},\,\pm {\frac {1+3{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {1}{2}},\,\pm {\frac {5+{\sqrt {5}}}{4}},\,\pm {\frac {7+{\sqrt {5}}}{4}},\,\pm {\frac {5+3{\sqrt {5}}}{2}}\right),$
• $\left(\pm {\frac {1}{2}},\,\pm {\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {4+{\sqrt {5}}}{2}},\,\pm {\frac {4+3{\sqrt {5}}}{2}}\right),$
• $\left(\pm {\frac {1}{2}},\,\pm {\frac {7+{\sqrt {5}}}{4}},\,\pm (2+{\sqrt {5}}),\,\pm {\frac {11+3{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {1}{2}},\,\pm {\frac {3+{\sqrt {5}}}{2}},\,\pm {\frac {7+3{\sqrt {5}}}{4}},\,\pm {\frac {13+3{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {1}{2}},\,\pm {\frac {5+3{\sqrt {5}}}{4}},\,\pm (2+{\sqrt {5}}),\,\pm 5{\frac {1+{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {1}{2}},\,\pm (1+{\sqrt {5}}),\,\pm {\frac {7+3{\sqrt {5}}}{4}},\,\pm {\frac {7+5{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm 3{\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {3+{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {13+5{\sqrt {5}}}{4}},\,\pm {\frac {2+{\sqrt {5}}}{2}}\right),$
• $\left(\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {5+3{\sqrt {5}}}{4}},\,\pm {\frac {7+3{\sqrt {5}}}{4}},\,\pm {\frac {5+2{\sqrt {5}}}{2}}\right),$
• $\left(\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm 1,\,\pm {\frac {5+3{\sqrt {5}}}{4}},\,\pm {\frac {7+2{\sqrt {5}}}{2}}\right),$
• $\left(\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {\sqrt {5}}{2}},\,\pm (1+{\sqrt {5}}),\,\pm {\frac {11+5{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {1+3{\sqrt {5}}}{4}},\,\pm {\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {5+3{\sqrt {5}}}{2}}\right),$
• $\left(\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {7+{\sqrt {5}}}{4}},\,\pm {\frac {4+{\sqrt {5}}}{2}},\,\pm (3+{\sqrt {5}})\right),$
• $\left(\pm 1,\,\pm {\frac {\sqrt {5}}{2}},\,\pm 3{\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {9+5{\sqrt {5}}}{4}}\right),$
• $\left(\pm 1,\,\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {7+3{\sqrt {5}}}{4}},\,\pm {\frac {4+3{\sqrt {5}}}{2}}\right),$
• $\left(\pm 1,\,\pm {\frac {5+3{\sqrt {5}}}{4}},\,\pm {\frac {11+3{\sqrt {5}}}{4}},\,\pm {\frac {3+2{\sqrt {5}}}{2}}\right),$
• $\left(\pm 1,\,\pm {\frac {4+{\sqrt {5}}}{2}},\,\pm {\frac {7+5{\sqrt {5}}}{4}},\,\pm {\frac {7+3{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {\sqrt {5}}{2}},\,\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {5+3{\sqrt {5}}}{2}},\,\pm 3{\frac {1+{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {\sqrt {5}}{2}},\,\pm {\frac {5+{\sqrt {5}}}{4}},\,\pm {\frac {7+5{\sqrt {5}}}{4}},\,\pm (2+{\sqrt {5}})\right),$
• $\left(\pm {\frac {\sqrt {5}}{2}},\,\pm 3{\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {5+3{\sqrt {5}}}{4}},\,\pm (3+{\sqrt {5}})\right),$
• $\left(\pm {\frac {\sqrt {5}}{2}},\,\pm {\frac {3+{\sqrt {5}}}{2}},\,\pm {\frac {11+3{\sqrt {5}}}{4}},\,\pm 3{\frac {3+{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {3}{2}},\,\pm {\frac {7+3{\sqrt {5}}}{4}},\,\pm (3+{\sqrt {5}})\right),$
• $\left(\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {1+{\sqrt {5}}}{2}},\,\pm {\frac {5+2{\sqrt {5}}}{2}},\,\pm 5{\frac {1+{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {1+{\sqrt {5}}}{2}},\,\pm {\frac {7+2{\sqrt {5}}}{2}},\,\pm 3{\frac {1+{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {7+{\sqrt {5}}}{4}},\,\pm {\frac {7+5{\sqrt {5}}}{4}},\,\pm 3{\frac {3+{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm 3{\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {3+{\sqrt {5}}}{2}},\,\pm {\frac {4+3{\sqrt {5}}}{2}}\right),$
• $\left(\pm {\frac {3}{2}},\,\pm {\frac {5+{\sqrt {5}}}{4}},\,\pm {\frac {11+5{\sqrt {5}}}{4}},\,\pm {\frac {3+{\sqrt {5}}}{2}}\right),$
• $\left(\pm {\frac {3}{2}},\,\pm {\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {5+2{\sqrt {5}}}{2}},\,\pm {\frac {3+2{\sqrt {5}}}{2}}\right),$
• $\left(\pm {\frac {3}{2}},\,\pm {\frac {3+{\sqrt {5}}}{2}},\,\pm {\frac {9+5{\sqrt {5}}}{4}},\,\pm {\frac {5+3{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {1+{\sqrt {5}}}{2}},\,\pm {\frac {5+{\sqrt {5}}}{4}},\,\pm {\frac {4+3{\sqrt {5}}}{2}},\,\pm {\frac {5+3{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {1+{\sqrt {5}}}{2}},\,\pm {\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {13+3{\sqrt {5}}}{4}},\,\pm {\frac {7+3{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {1+{\sqrt {5}}}{2}},\,\pm {\frac {7+{\sqrt {5}}}{4}},\,\pm {\frac {9+5{\sqrt {5}}}{4}},\,\pm {\frac {4+{\sqrt {5}}}{2}}\right),$
• $\left(\pm {\frac {5+{\sqrt {5}}}{4}},\,\pm (1+{\sqrt {5}}),\,\pm 3{\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {3+2{\sqrt {5}}}{2}}\right),$
• $\left(\pm {\frac {1+3{\sqrt {5}}}{4}},\,\pm {\frac {4+{\sqrt {5}}}{2}},\,\pm {\frac {7+3{\sqrt {5}}}{4}},\,\pm (2+{\sqrt {5}})\right),$
• $\left(\pm {\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {3+{\sqrt {5}}}{2}},\,\pm 5{\frac {1+{\sqrt {5}}}{4}},\,\pm 3{\frac {3+{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {5+3{\sqrt {5}}}{4}},\,\pm (1+{\sqrt {5}}),\,\pm {\frac {11+3{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {7+{\sqrt {5}}}{4}},\,\pm 3{\frac {1+{\sqrt {5}}}{4}},\,\pm (2+{\sqrt {5}}),\,\pm {\frac {3+2{\sqrt {5}}}{2}}\right),$
• $\left(\pm 3{\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {3+{\sqrt {5}}}{2}},\,\pm {\frac {7+5{\sqrt {5}}}{4}},\,\pm {\frac {4+{\sqrt {5}}}{2}}\right).$

External links

• Bowers, Jonathan. "Category 9: Omnitruncates" (#337).

• Klitzing, Richard. "goquidipdy".