Conditions for polygonal lines and polyhedra in \(E^ 3\) to be closed (Q1074871)

A polygon in \(E^ 3\) is determined up to Euclidean motion by the curvature angles, the torsion angles and the lengths of the segments. Similarly the question whether or not such a polygon is closed can be decided by certain determinants in terms of these quantities. This is the main result of the paper. Finally the author mentions the zig-zag polygons on the five Platonic solids which usually are called ''Petrie polygons''.