| Vertices: | 60 (60[4]) |
| Faces: | 54 (30 squares + 12 regular pentagons
+ 12 regular pentagrams) |
| Edges: | 120 |
| Symmetry: | Full Icosahedral (Ih) |
| Pentagon-Square Angle: | acos(−sqrt(10*(5−sqrt(5)))/10) | ≈121.717474411 degrees |
| Pentagram-Square Angle: | acos(−sqrt(10*(5+sqrt(5)))/10) | ≈148.282525589 degrees |
| Dual Solid: | Medial Deltoidal Hexecontahedron |
| (values below based on edge length = 1) |
| Circumscribed Radius: | sqrt(7)/2 | ≈1.3228756555322952953 |
| Midscribed Radius: | sqrt(6)/2 | ≈1.2247448713915890491 |
| Pentagon Center Radius: | sqrt(5*(25−2*sqrt(5)))/10 | ≈1.0131106564684930953 |
| Square Center Radius: | sqrt(5)/2 | ≈1.1180339887498948482 |
| Pentagram Center Radius: | sqrt(5*(25+2*sqrt(5)))/10 | ≈1.2139220723547203751 |
| 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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