## Incidence graph of complement of $PG(3,2)$

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 |