| Vertices: | 16 (8[3] + 8[5]) |
| Faces: | 16 (8 equilateral triangles + 8 mirror-symmetric pentagons) |
| Edges: | 32 (8 short + 8 medium + 16 long) |
| Symmetry: | 4-fold Antiprismatic (D4v) |
| Dihedral Angle 1 (8): | acos(sqrt(21*(5+4*sqrt(2)))/21) | ≈44.572027582 degrees |
| Dihedral Angle 2 (8): | acos(−(2*sqrt(2)−1)/7) | ≈105.141507814 degrees |
| Dihedral Angle 3 (8): | acos(−(2*sqrt(2)−1)/3) | ≈127.551602906 degrees |
| Dihedral Angle 4 (8): | acos(−(2*sqrt(2)−1)/7) | ≈254.858492186 degrees |
| Dual Toroid: | Square Antiprism-Trapezohedron Toroid (itself) |
| (values below based on a Square Antiprism with edge length = 1) |
| Short Edge (8): | sqrt(5*sqrt(2)−7) | ≈0.26658546821887205787 |
| Medium Edge (8): | sqrt(sqrt(2)−1) | ≈0.64359425290558262474 |
| Long Edge (16): | 1 |
| [3]-Vertex Radius (8): | sqrt(6*(3*sqrt(2)−4))/4 | ≈0.30164591439257374749 |
| [5]-Vertex Radius (8): | sqrt(2*(4+sqrt(2)))/4 | ≈0.82266438800803628873 |
| Volume: | 2*sqrt(2*(3*sqrt(2)−4))/3 | ≈0.464414266332008698248 |
| References: | [1] | Paul Gailiunas, Some Self-reciprocal Polyhedra. |
| [2] | T. Bakos, Octahedra Inscribed in a Cube,
The Mathematical Gazette 43 (1959), 17-20. |
|