| Vertices: | 24 (24[4]) |
| Faces: | 20 (8 equilateral triangles + 6 squares
+ 6 regular octagrams) |
| Edges: | 48 |
| Symmetry: | Full Octahedral (Oh) |
| Octagram-Square Angle: | acos(0) | 90 degrees |
| Octagram-Triangle Angle: | acos(sqrt(3)/3) | ≈125.264389683 degrees |
| Dual Solid: | Great Hexacronic Icositetrahedron |
| (values below based on edge length = 1) |
| Circumscribed Radius: | sqrt(5−2*sqrt(2))/2 | ≈0.73681287910395029658 |
| Midscribed Radius: | sqrt(2*(2−sqrt(2)))/2 | ≈0.54119610014619698440 |
| Square Center Radius: | (sqrt(2)−1)/2 | ≈0.20710678118654752440 |
| Triangle Center Radius: | (3*sqrt(3)−sqrt(6))/6 | ≈0.45777711332057563040 |
| Octagram Center Radius: | 1/2 | 0.5 |
| 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. |
|