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In this paper, a novel topological structured pattern, dubbed a spiral facet, is proposed and applied for the encoding and alignment of 3D facial triangular mesh surfaces. After describing the foundation of this representation, we present two direct face alignment methods, that exploit the ordered structure of the spiral facet in addressing the correspondence problem. We study the behavior and the performance of these two methods through experimentation conducted with a subset of a 3D face database. We also showcase the potential of our alignment framework for face recognition.