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

Abstract

Let Hn, 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 H4. We use this classification to study isometric full embeddings of H4 into DQ(8,2) and DH(7,4). We show that there is up to isomorphism a unique isometric full embedding of H4 into each of these dual polar spaces. Further applications are expected in the classification of dense near polygons with lines of size 3.