Abstract: In this paper, we present the Symmetry Descriptors of a 3D model. This is a collection of spherical functions that describes the measure of a model's rotational and reflective symmetry with respect to every axis passing through the center of mass. We show that Symmetry Descriptors can be computed efficiently using fast signal processing techniques, and demonstrate the empirical value of Symmetry Descriptors by showing that they improve matching performance in a variety of shape retrieval experiments.