| 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*(38*sqrt(3)−63))/3) | ≈14.261802346 degrees |
| Dihedral Angle 2 (24): | acos(−sqrt(3)/3) | ≈125.264389683 degrees |
| Dihedral Angle 3 (12): | acos(−(2*sqrt(3)−1)/3) | ≈214.778108668 degrees |
| Dual Toroid: | Hexagonal Trapezohedron-Antiprism Toroid (itself) |
| (values below based on a Hexagonal Antiprism with edge length = 2) |
| Short Edge (12): | sqrt(6*(11*sqrt(3)−19)) | ≈0.56156326406372182922 |
| Medium Edge (12): | 2*sqrt(211*sqrt(3)−365) | ≈1.3604710905169707931 |
| Long Edge (24): | 2 |
| [5]-Vertex Radius (12): | sqrt(3+sqrt(3)) | ≈2.1753277471610748738 |
| [3]-Vertex Radius (12): | sqrt(3*(57*sqrt(3)−97)) | ≈2.2761124959628021851 |
| Volume: | 4*sqrt(6*(775643*sqrt(3)−1343453)) | ≈2.8487495646855335448 |
| 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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