A lattice theoretical construction of a GAB of the Suzuki sporadic simple group (Q1097514)

GABs \((=\) geometries that are almost buildings) are Buekenhout-Tits geometries in which all rank 2 residual geometries are generalized polygons, except that they need not satisfy the intersection property. The two known examples of finite GABs with flag-transitive automorphism groups and the diagram of affine type arise from sporadic simple groups. One of them was constructed from the Lyons-Sims group, the other was associated with the Suzuki sporadic simple group Suz. The present paper provides a non-group-theoretical description of the GAB associated with Suz, using natural notions with respect to the complex Leech lattice. Furthermore a new existence proof of Suz as well as explicit and elementary proofs of some properties of Suz are given.