Symmetry of shape charts

For subdivision surfaces, the so-called shape chart can be used to characterize the curvature behavior at an extraordinary point a priori from the initial control net. Of late, it has been used in different approaches to tune subdivision algorithms to handle the so-called hybrid shapes. For this the shape charts are computed numerically. In this paper, symmetries of shape charts are analyzed that can be used to simplify the computations and to reduce the computation costs significantly.