On the universal embedding of the near hexagon related to the extended ternary Golay code

Let E1 be the near hexagon on 729 points related to the extended ternary Golay code. We prove in an entirely geometric way that the generating and embedding ranks of E1 are equal to 24. We also study the structure of the universal embedding e˜ of E1. More precisely, we consider several nice subgeometries A of E1 and determine which kind of embedding e˜A is, where e˜A is the embedding of A induced by e˜.