  Within the framework of the probability representation of quantum mechanics,
we study a superposition of generic Gaussian states associated to symmetries of
a regular polygon of n sides; in other words, the cyclic groups (containing the
rotational symmetries) and dihedral groups (containing the rotational and
inversion symmetries). We obtain the Wigner functions and tomographic
probability distributions (symplectic and optical tomograms) determining the
density matrices of the states explicitly as the sums of Gaussian terms. The
obtained Wigner functions demonstrate nonclassical behavior, i.e., contain
negative values, while the tomograms show a series of maxima and minima
different for each state, where the number of the critical points reflects the
order of the group defining the states. We discuss general properties of such a
generalization of normal probability distributions.
