| Vertices: | 48 (48[3]) |
| Faces: | 20 (8 regular hexagons + 6 regular octagons + 6 regular octagrams) |
| Edges: | 72 |
| Symmetry: | Full Octahedral (Oh) |
| Octagon-Hexagon Angle: | acos(sqrt(3)/3) | ≈54.735610317 degrees |
| Octagon-Octagram Angle: | acos(0) | 90 degrees |
| Octagram-Hexagon Angle: | acos(−sqrt(3)/3) | ≈125.264389683 degrees |
| Dual Solid: | Tetradyakis Hexahedron |
| (values below based on edge length = 1) |
| Circumscribed Radius: | sqrt(7)/2 | ≈1.3228756555322952953 |
| Midscribed Radius: | sqrt(6)/2 | ≈1.2247448713915890491 |
| Octagon Center Radius: | (sqrt(2)−1)/2 | ≈0.20710678118654752440 |
| Hexagon Center Radius: | sqrt(3)/2 | ≈0.86602540378443864676 |
| Octagram Center Radius: | (1+sqrt(2))/2 | ≈1.2071067811865475244 |
| References: | [1] | Jean Paul Albert Badoureau, Mémoire sur les Figures Isocèles,
Journal de l'École polytechnique 49 (1881), 47-172. |
| [2] | Johann Pitsch, Über Halbreguläre Sternpolyeder,
Zeitschrift für das Realschulwesen 6 (1881), 9-24, 64-65, 72-89, 216. |
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