| Vertices: | 10 (10[4]) |
| Faces: | 12 (10 equilateral triangles + 2 regular pentagrams) |
| Edges: | 20 |
| Symmetry: | 5-fold Antiprismatic (D5v) |
| Pentagram-Triangle Angle: | acos(sqrt(15*(5+2*sqrt(5)))/15) | ≈37.377368141 degrees |
| Triangle-Triangle Angle: | acos(sqrt(5)/3) | ≈318.189685104 degrees |
| Dual Solid: | Pentagrammic Concave Trapezohedron |
| (values below based on edge length = 1) |
| Circumscribed Radius: | sqrt(2*(5−sqrt(5)))/4 | ≈0.58778525229247312917 |
| Midscribed Radius: | (sqrt(5)−1)/4 | ≈0.30901699437494742410 |
| Pentagram Center Radius: | sqrt(10*(5−sqrt(5)))/20 | ≈0.26286555605956680301 |
| Triangle Center Radius: | −(3*sqrt(3)−sqrt(15))/12 | ≈−0.11026408970826791628 |
| References: | [1] | Jean Paul Albert Badoureau, Mémoire sur les Figures Isocèles,
Journal de l'École polytechnique 49 (1881), 47-172. |
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