| Vertices: | 24 (12[3] + 12[5]) |
| Faces: | 24 (12 equilateral triangles + 12 mirror-symmetric pentagons) |
| Edges: | 48 (12 short + 12 medium + 24 long) |
| Symmetry: | 6-fold Antiprismatic (D6v) |
| Dihedral Angle 1 (12): | acos(sqrt(3+2*sqrt(3))/3) | ≈32.060660106 degrees |
| Dihedral Angle 2 (12): | acos(−sqrt(3)/3) | ≈125.264389683 degrees |
| Dihedral Angle 3 (12): | acos(−(2*sqrt(3)−1)/3) | ≈145.221891332 degrees |
| Dihedral Angle 4 (12): | acos(−sqrt(3)/3) | ≈234.735610317 degrees |
| Dual Toroid: | Hexagonal Antiprism-Trapezohedron Toroid (itself) |
| (values below based on a Hexagonal Antiprism with edge length = 1) |
| Short Edge (12): | sqrt(3*sqrt(3)−5) | ≈0.44289098286895826186 |
| Medium Edge (12): | sqrt(2*(sqrt(3)−1))/2 | ≈0.60500033370605560912 |
| Long Edge (24): | 1 |
| [3]-Vertex Radius (12): | sqrt(3*(sqrt(3)−1))/2 | ≈0.74097105589669153429 |
| [5]-Vertex Radius (12): | sqrt(3+sqrt(3))/2 | ≈1.0876638735805374369 |
| Volume: | sqrt(6*(3*sqrt(3)−5))/2 | ≈0.54242845985433675517 |
| 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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