This is the unique such graph which is distance-transitive. There are other examples: the corresponding designs were classified by V. Mavron and V. Tonchev (Journal of Geometry 67 (2000), 180–187). These graphs will (hopefully!) be added to this site in the near future.
| Number of vertices: | 54 |
| Diameter: | 4 |
| Intersection array: | {9,8,6,1;1,3,8,9} |
| Spectrum: | 91318016(−3)18(−9)1 |
| Automorphism group: | order 26.36 |
| Distance-transitive: | Yes |
| Bipartite, Antipodal |