On the development of closed convex curves on 3-polytopes
Let \(C=(c_ 0,...,c_{n-1})\) be a directed closed polygonal curve, with ``corners'' \(c_ i\), on the surface of a 3-polytope P. The surface angle \(\alpha_ i\) at \(c_ i\) is the sum of the interior angles from \(c_{i- 1}c_ i\) to \(c_ ic_{i+1}\) measured on the surface of P. The development of C is a drawing of the curve in the plane so that the interior angle between the two segments adjacent to the image of \(c_ i\) in the plane is precisely \(\alpha_ i.\) In ``A theorem on the development of closed convex curves'', Johns Hopkins Univ., Techn. Report JHU-87116 (1987), the authors show that the development of C does not self-intersect. Presently, they give a simpler proof of this result.
scientific article; zbMATH DE number 4111456