| Vertices: | 60 (60[4]) |
| Faces: | 52 (20 equilateral triangles + 12 regular pentagons
+ 20 regular hexagons) |
| Edges: | 120 |
| Symmetry: | Full Icosahedral (Ih) |
| Hexagon-Pentagon Angle: | acos(sqrt(15*(5−2*sqrt(5)))/15) | ≈79.187683036 degrees |
| Hexagon-Triangle Angle: | acos(sqrt(5)/3) | ≈318.189685104 degrees |
| Dual Solid: | Great Icosacronic Hexecontahedron |
| (values below based on edge length = 1) |
| Circumscribed Radius: | sqrt(2*(17−3*sqrt(5)))/4 | ≈1.1342285961998925302 |
| Midscribed Radius: | sqrt(6*(5−sqrt(5)))/4 | ≈1.0180739209102543669 |
| Hexagon Center Radius: | (sqrt(15)−sqrt(3))/4 | ≈0.53523313465963489791 |
| Pentagon Center Radius: | sqrt(10*(65−19*sqrt(5)))/20 | ≈0.750245100408926292247 |
| Triangle Center Radius: | (9*sqrt(3)−sqrt(15))/12 | ≈0.976289493492706563047 |
| References: | [1] | Jean Paul Albert Badoureau, Mémoire sur les Figures Isocèles,
Journal de l'École polytechnique 49 (1881), 47-172. |
|