Vertices: | 62 (30[4] + 20[6] + 12[10]) |
Faces: | 120 (obtuse triangles) |
Edges: | 180 (60 short + 60 medium + 60 long) |
Symmetry: | Full Icosahedral (Ih) |
Dihedral Angle: | acos(−(179−24*sqrt(5))/241) | ≈121.336250807 degrees |
Dual Solid: | Great Truncated Icosidodecahedron |
(values below based on unit-edge-length Great Truncated Icosidodecahedron) |
Short Edge (60): | 3*sqrt(15*(65−19*sqrt(5)))/55 | ≈1.0023914607409093576 |
Medium Edge (60): | 2*sqrt(15*(5+sqrt(5)))/5 | ≈4.1673208594970816419 |
Long Edge (60): | sqrt(15*(85+31*sqrt(5)))/11 | ≈4.3738248570872609211 |
[10]-Vertex Radius (12): | 3*sqrt(5*(5−2*sqrt(5)))/5 | ≈0.97475908869871897847 |
[4]-Vertex Radius (30): | 3*(4*sqrt(5)−5)/11 | ≈1.0757105209088614870 |
[6]-Vertex Radius (20): | sqrt(15) | ≈3.8729833462074168852 |
Edge-scribed Radius: | sqrt(6*(5−2*sqrt(5)))/2 | ≈0.88982923502244570318 |
Inscribed Radius: | 3*sqrt(1205*(39−16*sqrt(5)))/241 | ≈0.77575035606720002909 |