| Vertices: | 12 (12[5]) |
| Faces: | 12 (regular pentagrams) |
| Edges: | 30 |
| Symmetry: | Full Icosahedral (Ih) |
| Dihedral Angle: | acos(−sqrt(5)/5) | ≈116.565051177 degrees |
| Dual Solid: | Great Dodecahedron |
| (values below based on edge length = 1) |
| Circumscribed Radius: | sqrt(2*(5−sqrt(5)))/4 | ≈0.58778525229247312917 |
| Midscribed Radius: | (sqrt(5)−1)/4 | ≈0.30901699437494742410 |
| Inscribed Radius: | sqrt(10*(5−sqrt(5)))/20 | ≈0.26286555605956680301 |
| References: | [1] | Johannes Kepler, Harmonices Mundi (1619). |
| [2] | Johannes Kepler with E. J. Aiton, A. M. Duncan,
and J. V. Field, translators, The Harmony of the World,
American Philosophical Society (1997). |
|