Great omnifacetopental trishecatonicosachoron

Great omnifacetopental trishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Gofapathi
Elements
Cells	120 icosidodecahedra 120 truncated great dodecahedra 120 small icosicosidodecahedra
Faces	1440 pentagrams 2400 triangles 720 pentagons 1440 decagons
Edges	3600
Vertices	720
Vertex figure	Faceted semi-uniform pentagonal prism, edge lengths (√5–1)/2 (base) and (1+√5)/2 (side)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {5+{\sqrt {5}}}{2}}}\approx 1.90211$
Hypervolume	$75{\frac {4+3{\sqrt {5}}}{2}}\approx 401.55765$
Number of external pieces	439680
Level of complexity	788
Related polytopes
Army	Rox
Regiment	Righi
Conjugate	Small polar facetopental trishecatonicosachoron
Convex core	Hecatonicosachoron
Abstract & topological properties
Flag count	129600
Orientable	Yes
Properties
Symmetry	H4, order 14400
Flag orbits	9
Convex	No
Nature	Wild

The great omnifacetopental trishecatonicosachoron, or gofapathi, is a nonconvex uniform polychoron consisting of 120 icosidodecahedra, 120 truncated great dodecahedra, and 120 small icosicosidodecahedra. Five icosidodecahedra, 10 truncated great dodecahedra, and 10 small icosicosidodecahedra form each of its vertices.

Gallery

Vertex coordinates

The vertices are the same as those of the regiment colonel, the rectified great hecatonicosachoron.

External links

• Bowers, Jonathan. "Category 5: Pentagonal Rectates" (#99).