Great prismatohecatonicosintercepted dishecatonicosachoron

Great prismatohecatonicosintercepted dishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Gophinady
Elements
Cells	730 pentagonal prisms, 120 dodecadodecahedra, 120 great dodecicosidodecahedra, 120 great quasitruncated icosidodecahedra
Faces	1200 triangles, 3600 squares, 1440 pentagons, 1440 pentagrams, 1200 hexagons, 1440 decagrams
Edges	3600+7200
Vertices	3600
Vertex figure	Inverted wedge, edge lengths 1 (1), √2 (4), (1+√5)/2 (2), (√5–1)/2 (2), √3 (2), and √(5–√5)/2 (4)
Measures (edge length 1)
Circumradius	${\sqrt {10-4{\sqrt {5}}}}\approx 1.02749$
Hypervolume	$25{\frac {251-102{\sqrt {5}}}{2}}\approx 286.51333$
Dichoral angles	Gaddid–3–gaddid: 120°
	Gaddid–5/2–did: 72°
	Gaddid–10/3–gaquatid: 72°
	Gaquatid–6–gaquatid: 60°
	Did–5–pip: 54°
	Gaquatid–4–pip: $\arccos \left({\sqrt {\frac {5+{\sqrt {5}}}{10}}}\right)\approx 31.71747^{\circ }$
Related polytopes
Army	Semi-uniform srix
Regiment	Gwavathi
Conjugate	Hecatonicosintercepted prismatodishecatonicosachoron
Abstract & topological properties
Euler characteristic	2040
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Wild

The great prismatohecatonicosintercepted dishecatonicosachoron, or gophinady, is a nonconvex uniform polychoron that consists of 120 dodecadodecahedra, 120 great dodecicosidodecahedra, 720 pentagonal prisms, and 120 great quasitruncated icosidodecahedra. One dodecadodecahedron, two great dodecicosidodecahedra, two pentagonal prisms, and four great quasitruncated icosidodecahedra join at each vertex.

Vertex coordinates

The vertices are the same as those of the regiment colonel, the great sphenoverted trishecatonicosachoron.

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#296).