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{\bf Bart De Bruyn and Pieter Vandecasteele}
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{\bf The Valuations of the Near Octagon ${\Bbb I}_4$}
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The maximal and next-to-maximal subspaces of a nonsingular para\-bolic
quadric $Q(2n,2)$, $n \geq 2$, which are not contained in a given
hyperbolic quadric $Q^+(2n-1,2) \subset Q(2n,2)$ define a sub near
polygon ${\Bbb I}_n$ of the dual polar space $DQ(2n,2)$. It is known that
every valuation of $DQ(2n,2)$ induces a valuation of ${\Bbb I}_n$. In this
paper, we classify all valuations of the near octagon ${\Bbb I}_4$ and show
that they are all induced by a valuation of $DQ(8,2)$. We use this
classification to show that there exists up to isomorphism a unique
isometric full embedding of ${\Bbb I}_n$ into each of the dual polar spaces
$DQ(2n,2)$ and $DH(2n-1,4)$.
\bye