Bard College, Annandale-on-Hudson, NY 12504, e-mail: firstname.lastname@example.org
Abstract: The classical polyhedral Gauss-Bonnet Theorem for surfaces uses the angle defect to measure curvature. Using a natural stratification for all polyhedra (not necessarily manifolds), the angle defect is generalized to arbitrary polyhedra in all dimensions. A Gauss-Bonnet type theorem is then proved for arbitrary polyhedra, using a modified Euler characteristic based on this stratification rather than the standard Euler characteristic.
Keywords: polyhedra, Gauss-Bonnet Theorem, curvature, stratification, Euler characteristic
Classification (MSC91): 52A25
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