| Vertices: | 62 (20[3] + 30[4] + 12[5]) |
| Faces: | 60 (rhombi) |
| Edges: | 120 (equal length) |
| Symmetry: | Full Icosahedral (Ih) |
| Dihedral Angle 1 (60): | acos((sqrt(5)−1)/4) | 72 degrees |
| Dihedral Angle 2 (60): | acos(−(1+sqrt(5))/4) | 216 degrees |
| The dual has the same polyhedral graph as the Rhombicosidodecahedron |
| (values below based on edge length = 1) |
| Rhombus Length: | sqrt(10*(5+sqrt(5)))/5 | ≈1.7013016167040798644 |
| Rhombus Width: | sqrt(10*(5−sqrt(5)))/5 | ≈1.0514622242382672121 |
| [5]-Vertex Radius (12): | 1 |
| [4]-Vertex Radius (30): | sqrt(10*(5+sqrt(5)))/5 | ≈1.7013016167040798644 |
| [3]-Vertex Radius (20): | sqrt(15*(5+2*sqrt(5)))/5 | ≈2.3839634168752983689 |
| Volume: | 4*sqrt(2*(5+sqrt(5))) | ≈15.216904260722457154 |
| References: | [1] | H. Unkelbach, Die kantensymmetrischen, gleichkantigen Polyeder,
Deutsche Mathematik 5 (1940), 306-316. |
|