We investigate the use of multiple intrinsic geometric attributes, including angles, geodesic distances, and curvatures, for 3D face recognition, where each face is represented by a triangle mesh, preprocessed to possess a uniform connectivity. As invariance to facial expressions holds the key to improving recognition performance, we propose to train for the component-wise weights to be applied to each individual attribute, as well as the weights used to combine the attributes, in order to adapt to expression variations. Using the eigenface approach based on the training results and a nearest neighbor classifier, we report recognition results on the expression-rich GavabDB face database and the well-known Notre Dame FRGC 3D database. We also perform a cross validation between the two databases.