| Vertices: | 60 (60[4]) |
| Faces: | 44 (20 equilateral triangles + 12 regular pentagrams
+ 12 regular decagrams) |
| Edges: | 120 |
| Symmetry: | Full Icosahedral (Ih) |
| Decagram-Triangle Angle: | acos(−sqrt(15*(5−2*sqrt(5)))/15) | ≈100.812316964 degrees |
| Decagram-Pentagram Angle: | acos(−sqrt(5)/5) | ≈116.565051177 degrees |
| Dual Solid: | Great Dodecacronic Hexecontahedron |
| (values below based on edge length = 1) |
| Circumscribed Radius: | sqrt(11−4*sqrt(5))/2 | ≈0.71689052337174209824 |
| Midscribed Radius: | sqrt(2*(5−2*sqrt(5)))/2 | ≈0.51374314837300779674 |
| Decagram Center Radius: | sqrt(5−2*sqrt(5))/2 | ≈0.363271264002680442948 |
| Triangle Center Radius: | (2*sqrt(15)−3*sqrt(3))/6 | ≈0.42496904495136698163 |
| Pentagram Center Radius: | 3*sqrt(5*(5−2*sqrt(5)))/10 | ≈0.48737954434935948923 |
| 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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