The incidence graph of the complementary design of $PG(3,2)$ (and the distance-3 graph of its incidence graph). It is the unique distance-transitive incidence graph of a $(15,8,4)$-design.
| Number of vertices: | $30$ |
| Diameter: | $3$ |
| Intersection array: | $\{8,7,4;1,4,8\}$ |
| Spectrum: | $8^1 2^{14} (-2)^{14} (-8)^1$ |
| Automorphism group: | $\mathrm{PSL}(4,2).2 \cong S_8$ |
| Distance-transitive: | Yes |
| Bipartite |