Ten exceptional geometries from trivalent distance regular graphs
The author studies embeddings of point-line geometries \(\Gamma\) into projective spaces (mainly over the reals). In particular, it is investigated how the existence of a flag-transitive group action on \(\Gamma\) gives rise to homogeneous embeddings of \(\Gamma\) provided that \(\Gamma\) is self-polar. The results are then applied to ten exceptional small point-line geometries which arise from the classification of the trivalent distance regular graphs due to \textit{N. L. Biggs} and \textit{D. H. Smith} [Bull. Lond. Math. Soc. 3, 155-158 (1971; Zbl 0217.02404)]. These exceptional geometries include (the incidence graphs of) the Fano plane and the symplectic generalized quadrange over GF(2).
flag transitive self-polar bislim geometries
scientific article; zbMATH DE number 1889236