| Vertices: | 72 (24[3] + 24[3] + 24[3]) |
| Faces: | 38 (6 squares + 8 regular hexagons
+ 24 mirror-symmetric hexagons) |
| Edges: | 108 (24 short + 24 medium + 60 long) |
| Symmetry: | Full Octahedral (Oh) |
| (values below based on short edge length = 1) |
| Short Edge (24): | 1 |
| Medium Edge (24): | sqrt(6)/2 | ≈1.2247448713915890491 |
| Long Edge (60): | sqrt(6)−1 | ≈1.4494897427831780982 |
| Max Vertex Radius: | sqrt(57−2*sqrt(6))/2 | ≈3.6090518323527040959 |
| Edge-scribed Radius: | 5*sqrt(2)/2 | ≈3.5355339059327376220 |
| Volume: | 79+38*sqrt(6) | ≈172.08061022576076773 |
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