Abstract
In this paper, we construct and classify all ovoids and spreads of the known generalized hexagon of order 3 (the split Cayley hexagon H ( 3 ) ). We exhibit some unexpected and nice geometric properties. As an application, we provide an elementary and geometric construction of a G 2 ( 3 ) -GAB of type G ˜ 2 . We also exhibit new ovoid-spread pairings.
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