| 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(3*(65+2*sqrt(5)))/15) | ≈15.752734214 degrees |
| Dihedral Angle 2 (20): | acos(−sqrt(5)/5) | ≈116.565051177 degrees |
| Dihedral Angle 3 (10): | acos(−sqrt(5)/3) | ≈221.810314896 degrees |
| Dual Toroid: | Pentagonal Trapezohedron-Antiprism Toroid (itself) |
| (values below based on a Pentagonal Trapezohedron with short edge length = 2) |
| Short Edge (10): | 3−sqrt(5) | ≈0.76393202250021030359 |
| Medium Edge (10): | 2 |
| Long Edge (20): | 5−sqrt(5) | ≈2.7639320225002103036 |
| [5]-Vertex Radius (10): | sqrt(10*(5−sqrt(5)))/2 | ≈2.6286555605956680301 |
| [3]-Vertex Radius (10): | (sqrt(3)+sqrt(15))/2 | ≈2.8025170768881470894 |
| Volume: | 10*(5*sqrt(5)−9)/3 | ≈7.2677996249964949402 |
| References: | [1] | Paul Gailiunas, Some Self-reciprocal Polyhedra. |
| [2] | T. Bakos, Octahedra Inscribed in a Cube,
The Mathematical Gazette 43 (1959), 17-20. |
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