| Vertices: | 48 (24[5] + 24[5]) |
| Faces: | 74 (8 equilateral triangles + {24 * 2} isosceles triangles
+ 6 squares + 12 rhombi) |
| Edges: | 120 (24 short + 72 medium + 24 long) |
| Symmetry: | Chiral Octahedral (O) |
| (values below based on edge-scribed radius = 1) |
| Short Edge (24): | sqrt(root[12th-order polynomial]) | ≈0.49390993178924684283 |
| Medium Edge (72): | sqrt(root[12th-order polynomial]) | ≈0.544524142823027688148 |
| Long Edge (24): | sqrt(root[12th-order polynomial]) | ≈0.59513835385680853347 |
| Rhombus Length: | sqrt(root[12th-order polynomial]) | ≈0.80506794992098201281 |
| Rhombus Width: | sqrt(root[12th-order polynomial]) | ≈0.73341104742063943256 |
| Rhombus Angle: | acos(root[12th-order polynomial]) | ≈84.666585538 degrees |
| Edge-scribed Radius: | 1 |
| Volume: | sqrt(root[12th-order polynomial]) | ≈4.1109064172755174987 |