| Vertices: | 26 (12[4] + 8[6] + 6[8]) |
| Faces: | 48 (acute triangles) |
| Edges: | 72 (24 short + 24 medium + 24 long) |
| Symmetry: | Full Octahedral (Oh) |
| Dihedral Angle: | acos(−(71+12*sqrt(2))/97) | ≈155.082179617 degrees |
| Dual Solid: | Truncated Cuboctahedron |
| (values below based on unit-edge-length Truncated Cuboctahedron) |
| Short Edge (24): | 2*sqrt(3*(10−sqrt(2)))/7 | ≈1.4500488186822163018 |
| Medium Edge (24): | 3*sqrt(6*(2+sqrt(2)))/7 | ≈1.9397429472460411059 |
| Long Edge (24): | 2*sqrt(6*(10+sqrt(2)))/7 | ≈2.3644524131865197592 |
| [4]-Vertex Radius (12): | 3*(4+sqrt(2))/7 | ≈2.3203772410170407352 |
| [6]-Vertex Radius (8): | sqrt(6) | ≈2.4494897427831780982 |
| [8]-Vertex Radius (6): | 3*(2+3*sqrt(2))/7 | ≈2.6754174373368364913 |
| Edge-scribed Radius: | sqrt(6*(2+sqrt(2)))/2 | ≈2.2630334384537146236 |
| Inscribed Radius: | sqrt(1746*(15+8*sqrt(2)))/97 | ≈2.2097412102566332828 |
| Volume: | 144*(1+sqrt(2))/7 | ≈49.663821854532241004 |
| 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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