| Vertices: | 20 (10[3] + 10[5]) |
| Faces: | 20 (10 equilateral triangles + 10 mirror-symmetric pentagons) |
| Edges: | 40 (10 short + 10 medium + 20 long) |
| Symmetry: | 5-fold Antiprismatic (D5v) |
| Dihedral Angle 1 (10): | acos(sqrt(15*(5+2*sqrt(5)))/15) | ≈37.377368141 degrees |
| Dihedral Angle 2 (10): | acos(−sqrt(5)/5) | ≈116.565051177 degrees |
| Dihedral Angle 3 (10): | acos(−sqrt(5)/3) | ≈138.189685104 degrees |
| Dihedral Angle 4 (10): | acos(−sqrt(5)/5) | ≈243.434948823 degrees |
| Dual Toroid: | Pentagonal Antiprism-Trapezohedron Toroid (itself) |
| (values below based on a Pentagonal Antiprism with edge length = 1) |
| Short Edge (10): | (3−sqrt(5))/2 | ≈0.38196601125010515180 |
| Medium Edge (10): | (sqrt(5)−1)/2 | ≈0.61803398874989484820 |
| Long Edge (20): | 1 |
| [3]-Vertex Radius (10): | (sqrt(15)−sqrt(3))/4 | ≈0.53523313465963489791 |
| [5]-Vertex Radius (10): | sqrt(2*(5+sqrt(5)))/4 | ≈0.95105651629515357212 |
| Volume: | 5*(sqrt(5)−1)/12 | ≈0.51502832395824570684 |
| References: | [1] | Paul Gailiunas, Some Self-reciprocal Polyhedra. |
| [2] | T. Bakos, Octahedra Inscribed in a Cube,
The Mathematical Gazette 43 (1959), 17-20. |
|