Due to the three axes x, y, and z, the apparent symmetry of various polar shapes and equations such as limacon, lemniscate, rose, cardiod, etc., and the "shapes" of electron orbitals deemed s, p, d, or f, is it possible that polar equations could describe the approximate location of electrons within these electron shell groups? Has it been tried/attempted already?

i thought the orbits were just described by probabilitiy densities. [but i might be wrong as i am not a physicist.]