| Vertices: | 26 (8[3] + 6[4] + 12[4]) |
| Faces: | 24 (tri-equiangular kites) |
| Edges: | 48 (24 short + 24 long) |
| Symmetry: | Full Octahedral (Oh) |
| Dihedral Angle: | acos(−(7+4*sqrt(2))/17) | ≈138.117959056 degrees |
| Dual Solid: | Rhombicuboctahedron |
| (values below based on unit-edge-length Rhombicuboctahedron) |
| Short Edge (24): | 2*sqrt(10−sqrt(2))/7 | ≈0.83718607580427642316 |
| Long Edge (24): | sqrt(2*(2−sqrt(2))) | ≈1.0823922002923939688 |
| Kite Length: | 2*sqrt(31−8*sqrt(2))/7 | ≈1.2676924722362712507 |
| Kite Width: | sqrt(2) | ≈1.4142135623730950488 |
| [3]-Vertex Radius (8): | (4*sqrt(3)+sqrt(6))/7 | ≈1.3396704247226696103 |
| [4]-Vertex Radius (18): | sqrt(2) | ≈1.4142135623730950488 |
| Edge-scribed Radius: | sqrt(2*(2+sqrt(2)))/2 | ≈1.3065629648763765279 |
| Inscribed Radius: | sqrt(34*(7+4*sqrt(2)))/17 | ≈1.2202629537976100741 |
| Volume: | 16*(1+2*sqrt(2))/7 | ≈8.7506905708484345088 |
| References: | [1] | Eugène Catalan, Mémoire sur la Théorie des Polyèdres,
Journal de l'École polytechnique 41 (1865), 1-71, +7 plates. |
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