The first complete characterization of a dendritic microstructure is presented. The dendrite morphology is obtained via a novel serial-sectioning process that allows the three-dimensional microstructure of opaque materials to be determined in a routine manner. Using the reconstructed dendrite we determine the spatial distribution of the mean and Gaussian curvature as well as the probability density distributions of these curvatures. These measurements yield many insights into the local processes that shape these topologically complex structures that are vital in setting many material properties.