The valuations of the near octagon G4G4

In De Bruyn (2003) [4] it was shown that the dual polar space DH(2n−1,4)DH(2n−1,4), n≥2n≥2, has a sub-near 2n2n-gon GnGn with a large automorphism group. In this paper, we classify the valuations of the near octagon G4G4. We show that each such valuation is either classical, the extension of a non-classical valuation of a G3G3-hex or is associated with a valuation of Fano-type of an H3H3-hex. In order to describe the latter type of valuation we must study the structure of G4G4 with respect to an H3H3-hex. This study also allows us to construct new hyperplanes of G4G4. We also show that each valuation of G4G4 is induced by a (classical) valuation of the dual polar space DH(7,4)DH(7,4).