Isometric embeddings of the near polygons Hn and Gn into dual polar spaces

We prove that for every n∈N∖{0,1} there exists up to isomorphism a unique isometric embedding of the near polygon Hn into the dual polar space DW(2n−1,2) and a unique isometric embedding of the near polygon Gn into the dual polar space DH(2n−1,4).