Angle counts for isothetic polygons and polyhedra

In the case of isothetic simple polyhedra there are only six different types of 3D angles. This article states and proofs a formula about counts of these angles. This complements formulas in combinatorial topology such as Euler's polyhedron formula, or the previously known formula on angle counts for isothetic polygons. The latter formula and the shown equality for angle counts of isothetic simple polyhedra are useful formulas for analyzing isothetic boundaries in 2D digital images (e.g. classification into inner (boundary of a hole) or outer boundaries, see [5]) and isothetic surfaces in 3D digital images (e.g. necessary condition for a complete surface scan). 1 Room 41/3675, 1 Microsoft Way Redmond, WA 98052, USA [email protected] 2 Center for Image Technology and Robotics Tamaki Campus, The University of Auckland, Auckland, New Zealand. [email protected] You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) days from the most recent time that you verified that this technical report is still available from the CITR Tamaki web site under terms that include this permission. All other rights are reserved by the author(s).