In this project, we are analyzing the 3D shapes of the occlusal surfaces of teeth, i.e. the surface that is predominantly used in chewing. We converted a dataset of 3D scans (see figure above) into a vector space representation, computed the average tooth (see Figure below), and performed a Principal Component Analysis (PCA) of the distribution of the examples in tooth-space. The first Principal Components are the directions of largest variance in the dataset, so they reflect the most significant degrees of freedom of dental shape.