In this paper, we developed a family of 2D and 3D invariant features with applications to 3D human faces recognition. The main contributions of this paper are: (a) systematically deriving a family of novel features, called summation invariant that are invariant to Euclidean transformation in both 2D and 3D; (b) developing an effective method to apply summation invariant to the 3D face recognition problem. Tested with the 3D data from the Face Recognition Grand Challenge