| Vertices: | 60 (60[4]) |
| Faces: | 62 (20 equilateral triangles + 30 squares
+ 12 regular pentagrams) |
| Edges: | 120 |
| Symmetry: | Full Icosahedral (Ih) |
| Square-Triangle Angle: | acos((sqrt(15)−sqrt(3))/6) | ≈69.094842552 degrees |
| Pentagram-Square Angle: | acos(sqrt(10*(5−sqrt(5)))/10) | ≈301.717474411 degrees |
| Dual Solid: | Great Deltoidal 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 |
| Square Center Radius: | (sqrt(5)−2)/2 | ≈0.11803398874989484820 |
| 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. |
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