| Vertices: | 120 (120[3]) |
| Faces: | 54 (30 squares + 12 regular decagons + 12 regular decagrams) |
| Edges: | 180 |
| Symmetry: | Full Icosahedral (Ih) |
| Decagon-Square Angle: | acos(sqrt(10*(5−sqrt(5)))/10) | ≈58.282525589 degrees |
| Decagon-Decagram Angle: | acos(sqrt(5)/5) | ≈63.434948823 degrees |
| Decagram-Square Angle: | acos(−sqrt(10*(5+sqrt(5)))/10) | ≈148.282525589 degrees |
| Dual Solid: | Medial Disdyakis Triacontahedron |
| (values below based on edge length = 1) |
| Circumscribed Radius: | sqrt(11)/2 | ≈1.6583123951776999246 |
| Midscribed Radius: | sqrt(10)/2 | ≈1.5811388300841896660 |
| Decagon Center Radius: | −sqrt(5−2*sqrt(5))/2 | ≈−0.363271264002680442948 |
| Square Center Radius: | 3/2 | 1.5 |
| Decagram Center Radius: | sqrt(5+2*sqrt(5))/2 | ≈1.5388417685876267013 |
| 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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