  A geometric view of the polarimetric properties of a nondepolarizing medium
is presented by means of a pair of vectors in the Poincar\'e sphere. An
alternative representation constituted by a set of vectors contained in the
equatorial plane of the Poincar\'e sphere is also defined and interpreted. The
analyses of the magnitudes and relative orientations of the constitutive
vectors of such simple representations allow for a classification of
nondepolarizing media.
