| Vertices: | 60 (60[3]) |
| Faces: | 24 (12 regular pentagons + 12 regular decagrams) |
| Edges: | 90 |
| Symmetry: | Full Icosahedral (Ih) |
| Decagram-Pentagon Angle: | acos(sqrt(5)/5) | ≈63.434948823 degrees |
| Decagram-Decagram Angle: | acos(−sqrt(5)/5) | ≈116.565051177 degrees |
| Dual Solid: | Great Pentakis Dodecahedron |
| (values below based on edge length = 1) |
| Circumscribed Radius: | sqrt(2*(17−5*sqrt(5)))/4 | ≈0.85291119940040149513 |
| Midscribed Radius: | (5−sqrt(5))/4 | ≈0.69098300562505257590 |
| Pentagon Center Radius: | sqrt(10*(65−29*sqrt(5)))/20 | ≈0.062054140173339523143 |
| Decagram Center Radius: | sqrt(2*(5−sqrt(5)))/4 | ≈0.58778525229247312917 |
| References: | [1] | Jean Paul Albert Badoureau, Mémoire sur les Figures Isocèles,
Journal de l'École polytechnique 49 (1881), 47-172. |
| [2] | Johann Pitsch, Über Halbreguläre Sternpolyeder,
Zeitschrift für das Realschulwesen 6 (1881), 9-24, 64-65, 72-89, 216. |
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