| Vertices: | 62 (20[3] + 30[4] + 12[5]) |
| Faces: | 60 (kites) |
| Edges: | 120 (60 short + 60 long) |
| Symmetry: | Full Icosahedral (Ih) |
| Dihedral Angle: | acos(−(19+8*sqrt(5))/41) | ≈154.121363126 degrees |
| Dual Solid: | Rhombicosidodecahedron |
| (values below based on unit-edge-length Rhombicosidodecahedron) |
| Short Edge (60): | sqrt(5*(85−31*sqrt(5)))/11 | ≈0.80499198439381116988 |
| Long Edge (60): | sqrt(5*(5−sqrt(5)))/3 | ≈1.2391601148672816338 |
| Kite Length: | sqrt(10*(157+31*sqrt(5)))/33 | ≈1.44160311266941938547 |
| Kite Width: | (5−sqrt(5))/2 | ≈1.3819660112501051518 |
| [3]-Vertex Radius (20): | (5*sqrt(3)+4*sqrt(15))/11 | ≈2.1956534020612776371 |
| [4]-Vertex Radius (30): | sqrt(5) | ≈2.2360679774997896964 |
| [5]-Vertex Radius (12): | sqrt(5*(5+2*sqrt(5)))/3 | ≈2.2939698674519558970 |
| Edge-scribed Radius: | sqrt(2*(5+2*sqrt(5)))/2 | ≈2.1762508994828215111 |
| Inscribed Radius: | sqrt(205*(19+8*sqrt(5)))/41 | ≈2.12099101951843341751 |
| Volume: | 100*(5+4*sqrt(5))/33 | ≈42.255369424239875108 |
| 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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