| Vertices: | 60 (60[4]) |
| Faces: | 44 (20 equilateral triangles + 12 regular pentagons
+ 12 regular decagrams) |
| Edges: | 120 |
| Symmetry: | Full Icosahedral (Ih) |
| Decagram-Pentagon Angle: | acos(−sqrt(5)/5) | ≈116.565051177 degrees |
| Decagram-Triangle Angle: | acos(−sqrt(15*(5+2*sqrt(5)))/15) | ≈142.622631859 degrees |
| Dual Solid: | Great Ditrigonal Dodecacronic Hexecontahedron |
| (values below based on edge length = 1) |
| Circumscribed Radius: | sqrt(2*(17−3*sqrt(5)))/4 | ≈1.1342285961998925302 |
| Midscribed Radius: | sqrt(6*(5−sqrt(5)))/4 | ≈1.0180739209102543669 |
| Pentagon Center Radius: | sqrt(10*(65−19*sqrt(5)))/20 | ≈0.750245100408926292247 |
| Decagram Center Radius: | sqrt(2*(5+sqrt(5)))/4 | ≈0.95105651629515357212 |
| Triangle Center Radius: | (9*sqrt(3)−sqrt(15))/12 | ≈0.976289493492706563047 |
| 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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