  The hemispherical Mueller matrix map for light reflected from a
plane-parallel planetary atmosphere is shown to obey several symmetry
properties that provide a straightforward method to check their physical
realizability. The mirror scattering relation and the reciprocity relation are
employed to support the symmetry rules for hemispherical Mueller matrix maps.
Additionally, two classes of experiments are identified in which the symmetry
rules can be applied, namely, when the incident beam is at zenith and off-
zenith angles and the scattering particles are spheres and randomly oriented
hexagonal particles.
