Coherent X-ray diffraction imaging at symmetric hhh Bragg reflections was used to resolve the structure of GaAs/In_0.15Ga_0.85As/GaAs core–shell–shell nanowires grown on a silicon (111) substrate. Diffraction amplitudes in the vicinity of GaAs 111 and GaAs 333 reflections were used to reconstruct the lost phase information. It is demonstrated that the structure of the core–shell–shell nanowire can be identified by means of phase contrast. Interestingly, it is found that both scattered intensity in the (111) plane and the reconstructed scattering phase show an additional threefold symmetry superimposed with the shape function of the investigated hexagonal nanowires. In order to find the origin of this threefold symmetry, elasticity calculations were performed using the finite element method and subsequent kinematic diffraction simulations. These suggest that a non-hexagonal (In,Ga)As shell covering the hexagonal GaAs core might be responsible for the observation.