The potassium trimer is investigated in its lowest electronic doublet states, employing several high-level ab initio methods (coupled cluster with single, double, and noniterative triple excitations, multiconfiguration self-consistent field, and multireference Rayleigh-Schrodinger perturbation theory of second order). One-dimensional cuts through the lowest 12 electronic states at C(2v) symmetry give insight in the complex electronic structure of the trimer, showing several (pseudo-)Jahn-Teller distortions that involve two or three excited states. Contour plots of the involved molecular orbitals are shown to prove the validity of the shell model frequently used for a qualitative description of metallic clusters.