The human external ears, or pinnae, have an intriguing shape and, like most parts of the human external body, bilateral symmetry is observed between left and right. It is a well-known part of our auditory sensory system and mediates the spatial localization of incoming sounds in 3D from monaural cues due to its shape-specific filtering as well as binaural cues due to the paired bilateral locations of the left and right ears. Another less broadly appreciated aspect of the human pinna shape is its uniqueness from one individual to another, which is on the level of what is seen in fingerprints and facial features. This makes pinnae very useful in human identification, which is of great interest in biometrics and forensics. Anatomically, the type of symmetry observed is known as matching symmetry, with structures present as separate mirror copies on both sides of the body, and in this work we report the first such investigation of the human pinna in 3D. Within the framework of geometric morphometrics, we started by partitioning ear shape, represented in a spatially dense way, into patterns of symmetry and asymmetry, following a two-factor ANOVA design. Matching symmetry was measured in all substructures of the pinna anatomy. However, substructures that 'stick out' such as the helix, tragus, and lobule also contained a fair degree of asymmetry. In contrast, substructures such as the conchae, antitragus, and antihelix expressed relatively stronger degrees of symmetric variation in relation to their levels of asymmetry. Insights gained from this study were injected into an accompanying identification setup exploiting matching symmetry where improved performance is demonstrated. Finally, possible implications of the results in the context of ear recognition as well as sound localization are discussed.