New near polygons from Hermitian varieties

Abstract

We define a new class of dense near polygons. The unique near $2n$-gon, $n \geq 0$, of this class will be denoted by $\G_n$. We will study the geodetically closed sub near polygons of $\G_n$. We will also determine the complete automorphism group and all spreads of symmetry. New glued near polygons can be constructed from these spreads of symmetry.