Great pentagonal hexecontahedron
|Great pentagonal hexecontahedron|
|Faces||60 mirror-symmetric pentagons|
|Vertex figure||20+60 triangles, 12 pentagrams|
|Measures (edge length 1)|
|Dihedral angle||≈ 104.43227°|
|Dual||Great snub icosidodecahedron|
|Abstract & topological properties|
|Symmetry||H3+, order 60|
If its dual, the great snub icosidodecahedron, has unit edge length, then the pentagon faces' short edges have approximate length 0.49069 (equal to a root of the polynomial ), and the long edges have approximate length 0.64563 (equal to a root of the polynomial ). The hexagons have four interior angles of , and one of , where is the negative root of the polynomial , and is the golden ratio.
A dihedral angle can be given as .
The inradius R ≈ 0.50974 of the great pentagonal hexecontahedron with unit edge length is equal to the square root of a real root of .