Möbius–Kantor graph

The Möbius-Kantor graph is the bipartite point-line incidence graph of the geometry with 8 points and 8 lines obtained by removing one point from the affine plane AG(2,3) of order 3. The Möbius-Kantor graph has spectrum ±31, (±√3)4, ±13, and is the unique graph with this spectrum. The graph is an antipodal 2-cover of the 3-cube. It is the unique 2-cover of the 3-cube without quadrangles, cf. BCN 9.2.10. One can add 8 edges and obtain the 4-cube (Coxeter).