3D imaging systems are used to construct high-resolution meshes of patient's heads that can be analyzed by computer algorithms. Our work starts with such 3D head meshes and produces both global and local descriptors of 3D shape. Since these descriptors are numeric feature vectors, they can be used in both classification and quantification of various different abnormalities. In this paper, we define these descriptors, describe our methodology for constructing them from 3D head meshes, and show through a set of classification experiments involving cases and controls for a genetic disorder called 22q11.2 deletion syndrome that they are suitable for use in craniofacial research studies. The main contributions of this work include: automatic generation of novel global and local data representations, robust automatic placement of anthropometric landmarks, generation of local descriptors for nasal and oral facial features from landmarks, use of local descriptors for predicting various local facial features, and use of global features for 22q11.2DS classification, showing their potential use as descriptors in craniofacial research.