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: | $9^1 3^{18} 0^{16} (-3)^{18} (-9)^1$ |
| Automorphism group: | order $2^6.3^6$ |
| Distance-transitive: | Yes |
| Bipartite, Antipodal |