The valuations of the near octagon G4

In De Bruyn (2003) [4] it was shown that the dual polar space DH(2n-1,4), n>=2, has a sub-near 2n-gon G"n with a large automorphism group. In this paper, we classify the valuations of the near octagon G"4. We show that each such valuation is either classical, the extension of a non-classical valuation of a G"3-hex or is associated with a valuation of Fano-type of an H"3-hex. In order to describe the latter type of valuation we must study the structure of G"4 with respect to an H"3-hex. This study also allows us to construct new hyperplanes of G"4. We also show that each valuation of G"4 is induced by a (classical) valuation of the dual polar space DH(7,4).