Summary: The maximal and next-to-maximal subspaces of a nonsingular parabolic 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 \({\mathbb I}_n\) of the dual polar space \(DQ(2n,2)\). It is known that every valuation of \(DQ(2n,2)\) induces a valuation of \({\mathbb I}_n\). In this paper, we classify all valuations of the near octagon \({\mathbb I}_4\) 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 \({\mathbb I}_n\) into each of the dual polar spaces \(DQ(2n,2)\) and \(DH(2n-1,4)\).