| Vertices: | 32 (20[3] + 12[10]) |
| Faces: | 60 (isosceles triangles) |
| Edges: | 90 (60 short + 30 long) |
| Symmetry: | Full Icosahedral (Ih) |
| Dihedral Angle: | acos(−3*(8+5*sqrt(5))/61) | ≈160.612552209 degrees |
| Dual Solid: | Truncated Dodecahedron |
| (values below based on unit-edge-length Truncated Dodecahedron) |
| Short Edge (60): | 5*(7+sqrt(5))/22 | ≈2.09910635852267947646 |
| Long Edge (30): | (5+sqrt(5))/2 | ≈3.6180339887498948482 |
| [3]-Vertex Radius (20): | 5*(3*sqrt(3)+2*sqrt(15))/22 | ≈2.9413907079821512843 |
| [10]-Vertex Radius (12): | sqrt(5*(5+2*sqrt(5)))/2 | ≈3.44095480117793384552 |
| Edge-scribed Radius: | (5+3*sqrt(5))/4 | ≈2.9270509831248422723 |
| Inscribed Radius: | 5*sqrt(61*(41+18*sqrt(5)))/122 | ≈2.8852583129200411870 |
| Volume: | 125*(19+9*sqrt(5))/44 | ≈111.14946533380144110 |
| 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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