This is the incidence graph of the complementary design of the biplane on 11 points, and thus the distance-3 graph of its incidence graph.
| Number of vertices: | $22$ |
| Diameter: | $3$ |
| Intersection array: | $\{6,5,3;1,3,6\}$ |
| Spectrum: | $6^1 (\sqrt{3})^{10} (-\sqrt{3})^{10} (-6)^1$ |
| Automorphism group: | $ PGL(2,11)$ |
| Distance-transitive: | Yes |
| Bipartite |