| Vertices: | 56 (8[3] + 24[3] + 24[3]) |
| Faces: | 30 (24 mirror-symmetric pentagons + 6 regular octagons) |
| Edges: | 84 (24 short + 60 long) |
| Symmetry: | Full Octahedral (Oh) |
| (values below based on long edge length = 1) |
| Short Edge (24): | 2−sqrt(2)+sqrt(10−7*sqrt(2)) | ≈0.90281177318911937654 |
| Long Edge (60): | 1 |
| Max Vertex Radius: | sqrt(2*(5+2*sqrt(2)+2*sqrt(2+sqrt(2))))/2 | ≈2.4004109288610707709 |
| Edge-scribed Radius: | (1+2*sqrt(2+sqrt(2)))/2 | ≈2.3477590650225735123 |
| Volume: | 26−sqrt(2)+8*sqrt(10−sqrt(2)) | ≈48.026996560146644800 |