  The symmetry properties of the resistance of mesoscopic samples in the
quantum Hall regime are investigated. In addition to the reciprocity relation,
our samples obey new symmetries, that relate resistances measured with
different contact configurations. Different kinds of symmetries are identified,
depending on whether the magnetic field value is such that the system is above,
or below, a quantum Hall transition. Related symmetries have recently been
reported for macroscopic samples in the quantum Hall regime by Ponomarenko {\it
et al.} (Solid State Commun. {\bf 130}, 705 (2004)), and Karmakar {\it et al.}
(Preprint cond-mat/0309694).
