The exceptional hyperplanes of DH(5,4)DH(5,4)

In [B. De Bruyn, H. Pralle, The hyperplanes of DH(5,q2)DH(5,q2), preprint 2005], we showed the existence of five isomorphism classes of hyperplanes in each dual polar space of type DH(5,q2)DH(5,q2). We also proved there that every hyperplane of DH(5,q2)DH(5,q2) belongs to one of these five classes if q≠2q≠2. In the present paper, we classify all hyperplanes of DH(5,4)DH(5,4) and find four additional isomorphism classes of hyperplanes.