We propose a deformation-based representation for analyzing expressions fromthree-dimensional (3D) faces. A point cloud of a 3D face is decomposed into an ordered deformable set of curves that start from a fixed point. Subsequently, a mapping function is defined to identify the set of curves with an element of a high-dimensional matrix Lie group, specifically the direct product of SE(3). Representing 3D faces as an element of a high-dimensional Lie group has two main advantages. First, using the group structure, facial expressions can be decoupled from a neutral face. Second, an underlying non-linear facial expression manifold can be captured with the Lie group and mapped to a linear space, Lie algebra of the group. This opens up the possibility of classifying facial expressions with linear models without compromising the underlying manifold. Alternatively, linear combinations of linearised facial expressions can be mapped back from the Lie algebra to the Lie group. The approach is tested on the Binghamton University 3D Facial Expression (BU-3DFE) and the Bosphorus datasets. The results show that the proposed approach performed comparably, on the BU-3DFE dataset, without using features or extensive landmark points.