| Vertices: | 74 (48[3] + 12[4] + 8[6] + 6[8]) |
| Faces: | 72 (24 short kites + 24 medium kites + 24 long kites) |
| Edges: | 144 (48 short + 48 medium + 48 long) |
| Symmetry: | Full Octahedral (Oh) |
| Long Edge Angle: | acos(−11/12) | ≈156.443535691 degrees |
| Medium Edge Angle: | acos(−(6+sqrt(2))/8) | ≈157.937808842 degrees |
| Short Edge Angle: | acos(−(10+sqrt(2))/12) | ≈162.023738221 degrees |
| (values below based on unit-edge-length Truncated Cuboctahedron) |
| Short Edge (48): | sqrt(109−6*sqrt(2))/14 | ≈0.71612163566688262435498 |
| Medium Edge (48): | sqrt(13−6*sqrt(2))/2 | ≈1.0623933623853066161 |
| Long Edge (48): | sqrt(23)*(3+sqrt(2))/14 | ≈1.5121303252188161974 |
| Short Kite Length: | 2*sqrt(3*(10−sqrt(2)))/7 | ≈1.4500488186822163018 |
| Short Kite Width: | 1 |
| Medium Kite Length: | 3*sqrt(6*(2+sqrt(2)))/7 | ≈1.9397429472460411059 |
| Medium Kite Width: | 1 |
| Long Kite Length: | 2*sqrt(6*(10+sqrt(2)))/7 | ≈2.3644524131865197592 |
| Long Kite Width: | 1 |
| [3]-Vertex Radius (48): | sqrt(13+6*sqrt(2))/2 | ≈2.3176109128927665138 |
| [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 |
| Inscribed Radius: | sqrt(6*(2+sqrt(2)))/2 | ≈2.2630334384537146236 |
| Volume: | 12*(12+13*sqrt(2))/7 | ≈52.088187961457546802 |