| Vertices: | 12 (6[3] + 6[5]) |
| Faces: | 12 (6 equilateral triangles + 6 mirror-symmetric pentagons) |
| Edges: | 24 (6 short + 6 medium + 12 long) |
| Symmetry: | 3-fold Antiprismatic (D3v) |
| Dihedral Angle 1 (6): | acos(5*sqrt(3)/9) | ≈15.793169048 degrees |
| Dihedral Angle 2 (12): | acos(0) | 90 degrees |
| Dihedral Angle 3 (6): | acos(−1/3) | ≈250.528779366 degrees |
| Dual Toroid: | Cube-Octahedron Toroid (itself) |
| (values below based on a Cube with edge length = 4) |
| Short Edge (6): | 1 |
| Medium Edge (6): | 4 |
| Long Edge (12): | 3*sqrt(2) | ≈4.2426406871192851464 |
| [5]-Vertex Radius (6): | 3 |
| [3]-Vertex Radius (6): | 2*sqrt(3) | ≈3.4641016151377545871 |
| Volume: | 19 [EXACT] |
| 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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