| Vertices: | 32 (12[5] + 20[6]) |
| Faces: | 60 (isosceles triangles) |
| Edges: | 90 (60 short + 30 long) |
| Symmetry: | Full Icosahedral (Ih) |
| Dihedral Angle: | acos(−(80+9*sqrt(5))/109) | ≈156.718553726 degrees |
| Dual Solid: | Truncated Icosahedron |
| (values below based on unit-edge-length Truncated Icosahedron) |
| Short Edge (60): | 9*(2*sqrt(5)−1)/19 | ≈1.6446959786840112913 |
| Long Edge (30): | 3*(sqrt(5)−1)/2 | ≈1.8541019662496845446 |
| [5]-Vertex Radius (12): | 9*sqrt(65+22*sqrt(5))/38 | ≈2.53092686862706152146 |
| [6]-Vertex Radius (20): | 3*sqrt(3)/2 | ≈2.5980762113533159403 |
| Edge-scribed Radius: | 3*(1+sqrt(5))/4 | ≈2.4270509831248422723 |
| Inscribed Radius: | 9*sqrt(109*(17+6*sqrt(5)))/218 | ≈2.3771316059838161118 |
| Volume: | 405*(9+sqrt(5))/76 | ≈59.876414880097563514 |
| References: | [1] | Eugène Catalan, Mémoire sur la Théorie des Polyèdres,
Journal de l'École polytechnique 41 (1865), 1-71, +7 plates. |
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