Great pentagrammic hexecontahedron
|Great pentagrammic hexecontahedron|
|Vertex figure||60+20 triangles, 12 pentagrams|
|Measures (edge length 1)|
|Dihedral angle||≈ 60.90113°|
|Dual||Great inverted retrosnub icosidodecahedron|
|Convex core||Pentagonal hexecontahedron|
|Abstract & topological properties|
|Symmetry||H3+, order 60|
It is the dual of the great inverted retrosnub icosidodecahedron.
Each pentagram has three long and two short edges; the ratio between them is given by , where , the largest positive root of the polynomial , and is the golden ratio. (The long edges' length is approximately 3.06368 or a root of the polynomial , and the short edges' length is approximately 1.72678 or a root of the polynomial .)
Each face has four equal angles of , and one angle of .
A dihedral angle is equal to .
The inradius R ≈ 0.14897 of a great pentagrammic hexecontahedron with unit edge length is equal to the square root of a root of the polynomial .