| Vertices: | 120 (120[3]) |
| Faces: | 62 (30 squares + 20 regular hexagons + 12 regular decagrams) |
| Edges: | 180 |
| Symmetry: | Full Icosahedral (Ih) |
| Hexagon-Square Angle: | acos((sqrt(15)−sqrt(3))/6) | ≈69.094842552 degrees |
| Decagram-Hexagon Angle: | acos(sqrt(15*(5−2*sqrt(5)))/15) | ≈79.187683036 degrees |
| Decagram-Square Angle: | acos(−sqrt(10*(5−sqrt(5)))/10) | ≈121.717474411 degrees |
| Dual Solid: | Great Disdyakis Triacontahedron |
| (values below based on edge length = 1) |
| Circumscribed Radius: | sqrt(31−12*sqrt(5))/2 | ≈1.0206841173941284126 |
| Midscribed Radius: | sqrt(6*(5−2*sqrt(5)))/2 | ≈0.88982923502244570318 |
| Hexagon Center Radius: | (sqrt(15)−2*sqrt(3))/2 | ≈0.20444086553483114906 |
| Square Center Radius: | (2*sqrt(5)−3)/2 | ≈0.73606797749978969641 |
| Decagram Center Radius: | sqrt(5*(5−2*sqrt(5)))/2 | ≈0.81229924058226581539 |
| 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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