Great inverted pentagonal hexecontahedron

Great inverted pentagonal hexecontahedron
(3D model) (OFF file)
Rank	3
Type	Uniform dual
Space	Spherical
Notation
Coxeter diagram	p5/3p3p
Elements
Faces	60 mirror-symmetric concave pentagons
Edges	30+60+60
Vertices	20+60+12
Vertex figure	20+60 triangles, 12 pentagrams
Measures (edge length 1)
Inradius	≈ 0.25744
Dihedral angle	≈ 78.35920°
Central density	13
Related polytopes
Dual	Great inverted snub icosidodecahedron
Abstract & topological properties
Flag count	600
Euler characteristic	2
Orientable	Yes
Genus	0
Properties
Symmetry	H3+, order 60
Convex	No
Nature	Tame

The great inverted pentagonal hexecontahedron is a uniform dual polyhedron. It consists of 60 mirror-symmetric concave pentagons, each with two short and three long edges.

If its dual, the great inverted snub icosidodecahedron, has unit edge length, then the pentagon faces' short edges have approximate length 0.23186 (equal to a root of the polynomial $31x^6-53x^5-26x^4+34x^3+17x^2-x-1$), and the long edges have approximate length 0.81801 (equal to a root of the polynomial $x^6-2x^5-4x^4+x^3+4x^2-1$).

A dihedral angle can be given as acos(α), where α ≈ 0.20178 is a real root of the polynomial $209x^6-94x^5-137x^4+100x^3-9x^2-6x+1$.

The inradius R ≈ 0.25744 of the great inverted pentagonal hexecontahedron with unit edge length is equal to the square root of a real root of $856064x^6-3900416x^5+1443072x^4-149376x^3+6384x^2-128x+1$.

External links

• Wikipedia Contributors. "Great inverted pentagonal hexecontahedron".
• McCooey, David. "Great Inverted Pentagonal Hexecontahedron"