The Valuations of the Near Octagon ${mathbb{H}}_4$

摘要

Let ${mathbb{H}}_n$ , n ≥ 2, be the near 2n-gon on the 2-factors of a complete graph with 2n + 2 vertices. In this paper, we classify the valuations of the near octagon ${mathbb{H}}_4$ . We use this classification to study isometric full embeddings of ${mathbb{H}}_4$ into DQ(8,2) and DH(7,4). We show that there is up to isomorphism a unique isometric full embedding of ${mathbb{H}}_4$ into each of these dual polar spaces. Further applications are expected in the classification of dense near polygons with lines of size 3.