This is the incidence graph of the unique symmetric transversal design $\mathrm{STD}_2[6;3]$.
| Number of vertices: | $36$ |
| Diameter: | $4$ |
| Intersection array: | $\{6,5,4,1;1,2,5,6\}$ |
| Spectrum: | $6^1 (\sqrt{6})^{12} 0^{10} (-\sqrt{6})^{12} (-6)^1$ |
| Automorphism group: | $3\cdot S_6.2$ |
| Distance-transitive: | Yes |
| Bipartite, Antipodal |