The exceptional hyperplanes of

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