# The Gauss map of polyhedral vertex stars

@inproceedings{Banchoff2019TheGM, title={The Gauss map of polyhedral vertex stars}, author={Thomas F. Banchoff and Felix Gunther}, year={2019} }

In discrete differential geometry, it is widely believed that the discrete Gaussian curvature of a polyhedral vertex star equals the algebraic area of its Gauss image. However, no complete proof has yet been described. We present an elementary proof in which we compare, for a particular normal vector, its winding numbers around the Gauss image and its antipode with its critical point index. This index is closely related to the normal degree of the Gauss map. We deduce how the number of… CONTINUE READING

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