A New Near Octagon and the Suzuki Tower

  • Anurag Bishnoi
  • Bart De Bruyn
Keywords: Near polygon, Generalized polygon, Suzuki tower, Strongly regular graphs, Commuting involutions


We 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 $(2,4)$.

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