This graph is the complement of the Johnson graph $\mathrm{J}(12,2)$.
| Number of vertices: | $66$ |
| Diameter: | $2$ |
| Intersection array: | $\{45,16;1,36\}$ |
| Spectrum: | $45^1 1^{54} (-9)^{11}$ |
| Automorphism group: | $\mathrm{S}_{12}$ |
| Distance-transitive: | Yes |
| Primitive |