The Angle Defect for Arbitrary Polyhedra

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

Full text of the article:

• Compressed DVI file (25325 Bytes)
• Compressed Postscript file (85062 Bytes)