This paper presents an approach to resolve the azimuth ambiguity of 3D Shape Contexts (3DSC) based on asymmetry patterns. We show that it is possible to provide rotational invariance to 3DSC at the expense of a marginal increase in computational load, outperforming previous algorithms dealing with the azimuth ambiguity. We build on a recently presented measure of approximate rotational symmetry in 2D defined as the overlapping area between a shape and rotated versions of itself to extract asymmetry patterns from a 3DSC in a variety of ways, depending on the spatial relationships that need to be highlighted or disabled. Thus, we define Asymmetry Patterns Shape Contexts (APSC) from a subset of the possible spatial relations present in the spherical grid of 3DSC; hence they can be thought of as a family of descriptors that depend on the subset that is selected. This provides great flexibility to derive different descriptors. We show that choosing the appropriate spatial patterns can considerably reduce the errors obtained with 3DSC when targeting specific types of points.