Two problems that are generally considered to be difficult in face recognition are variations in expression and distinguishing between the faces of identical twins. This work consists of a study on the performance of 3D face recognition algorithms on a relatively large set of identical twins: the 3D Twins Expression Challenge (“3D TEC’) dataset. The 3D TEC dataset is a challenging dataset that consists of 3D scans of 107 pairs of twins that were acquired in a single session, with each subject having a scan of a neutral expression and a smiling expression. The combination of factors related to the facial similarity of identical twins and the variation in facial expression makes this a challenging dataset. In this paper, we demonstrate the performance of modern face recognition algorithms on this dataset. The results indicate that 3D face recognition of identical twins in the presence of varying facial expressions is far from a solved problem. An approach based on dimensionality reduction of the geodesic distance matrix is also attempted against the dataset. It was found that the use of geodesic distances did not improve performance for a certain class of algorithms due to the reduction in resolution needed for calculating the geodesic distance matrix.