On the development of closed convex curves on 3-polytopes
type: Item
instance of: scholarly article
title: On the development of closed convex curves on 3-polytopes
zbMATH Open document ID: 0678.52004
DOI: 10.1007/BF01222270
author: Joseph O'Rourke
author: Catherine A. Schevon
published in: Journal of Geometry
publication date: 1989-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 52Bxx
Mathematics Subject Classification ID: 53A05
zbMATH DE Number: 4111456
zbMATH Keywords: polygonal curve
zbMATH Keywords: 3-polytope
zbMATH Keywords: development
reviewed by: T. Bisztriczky
MaRDI profile type: Publication
cites work: Q5524290
cites work: Geometrical problems concerning polyhedra in the large
full work available at URL: https://doi.org/10.1007/bf01222270
OpenAlex ID: W2316123560
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description: scientific article; zbMATH DE number 4111456