Shapes of the proton

A model proton wave function, constructed using Poincar\'e invariance and constrained by recent electromagnetic form factor data, is used to study the shape of the proton. Spin-dependent quark densities are defined as matrix elements of density operators in proton states of definite polarization, and shown to have an infinite variety of nonspherical shapes. For high momentum quarks with spin parallel to that of the proton, the shape resembles that of a peanut, but for quarks with antiparallel spin the shape is that of a bagel.