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The polarization of electromagnetic radiation reflected by a particulate surface is determined by a four by four reflection matrix. Symmetry relations are quite common for such reflection matrices. The reciprocity and mirror symmetry relations are combined to derive a third symmetry relation. These three relations are used to simplify reflection matrices for a variety of special directions of incident and reflected radiation. We show that some elements of the reflection matrix can vanish or equal other elements that have the same or opposite sign. Several applications of the results for studies of particulate surfaces and atmospheres above them are pointed out.The work of Olga Munoz has been supported by the Plan Nacional de Astronomia y Astrofisica contract AYA2015-67152-R.Peer reviewe

Symmetry and structure of reflection matrices of celestial bodies with particulate surfaces