A New Near Octagon and the Suzuki Tower
Keywords: Near polygon, Generalized polygon, Suzuki tower, Strongly regular graphs, Commuting involutions
AbstractWe construct and study a new near octagon of order $(2,10)$ which has its full automorphism group isomorphic to the group $G_2(4):2$ and which contains $416$ copies of the Hall-Janko near octagon as full subgeometries. Using this near octagon and its substructures we give geometric constructions of the $G_2(4)$-graph and the Suzuki graph, both of which are strongly regular graphs contained in the Suzuki tower. As a subgeometry of this octagon we have discovered another new near octagon, whose order is $(2,4)$.