In this paper, we introduce a new approach for partial 3D face recognition, which makes use of shape decomposition over the rigid1 part of a face. To explore the descriptiveness of shape dissimilarity over an isometric part of a face, which has lower probability to be influenced by expression, we transform a 3D shape to a 2D domain using conformal mapping and use shape decomposition as a similarity measurement. In our work we investigate several classifiers as well as several shape descriptors for recognition purposes. Recognition tests on a subset of the FRGC data set show approximately 80% rank-one recognition rate using only the eyes and nose part of the face.