In this paper we address the challenge of matching patient geometry to facilitate the design of patient treatment plans in radiotherapy. To this end we propose a novel shape descriptor, the Overlap Volume Histogram, which provides a rotation and translation invariant representation of a patient's organs at risk relative to the tumor volume. Using our descriptor, it is possible to accurately identify database patients with similar constellations of organ and tumor geometries, enabling the transfer of treatment plans between patients with similar geometries, We demonstrate the utility of our method for such tasks by outperforming state of the art shape descriptors in the retrieval of patients with similar treatment plans. We also preliminarily show its potential as a quality control tool by demonstrating how it is used to identify an organ at risk whose dose can be significantly reduced.