Geometric characterization of the sporadic groups Fi22, Fi23, and Fi24 - Pasechnik, Dmitrii V. (2013)
Let Σ1, …, Σ4 be the 3-transposition graphs for Fischer's sporadic groups Fi21, …, Fi24. We classify connected locally Σi graphs gQ = gQi+1 for i = 1, 2, 3. In the minimal case i = 1 we also assume that for every nondegenerate 4-circuit abcd the subgraph Θ(a, b, c, d) is isomorphic to the disjoint union of three copies of K3,3. If i = 1, 2 then Θ is isomorphic to Σi+1, whereas if i = 3 then Θ is isomorphic either to Σ4 or to its 3-fold antipodal cover 3Σ4.