There are exactly two rank-3 strongly regular graphs with parameters $(40,12,2,4)$. They are the two known $\mathrm{GQ}(3,3)$s, namely $\mathrm{O_5}(3)$ and $\mathrm{Sp}_4(3)$. They are the duals of each other. The graph $\mathrm{Sp}_4(3)$ is the same as the $\overline{\mathrm{NU}_4(2)}$ graph, which is the local graph of the $\overline{\mathrm{NU}_5(2)}$ graph.
| Number of vertices: | $40$ |
| Diameter: | $2$ |
| Intersection array: | $\{12,9;1,4\}$ |
| Spectrum: | $12^1 2^{24} (-4)^{15}$ |
| Automorphism group: | $\mathrm{PS_{p}}(4,3):2$ |
| Distance-transitive: | Yes |
| Primitive |