Planar polygons and hyperbolic polyhedra
type: Item
instance of: scholarly article
title: Planar polygons and hyperbolic polyhedra
zbMATH Open document ID: 0758.52001
DOI: 10.1007/BF00147868
author: Christophe Bavard
author: Étienne Ghys
published in: Geometriae Dedicata
publication date: 1993-01-16T00:00:00Z
review text: The authors consider the space of polygons in the Euclidean plane having fixed prescribed angles. These form a vector space on which the measurement of oriented area defines a quadratic form. In the case of convex polygons this construction is used to associate a convex polyhedron in a suitable hyperbolic space with the given space. The relations between the structure of this polyhedron and the geometry of the corresponding polygons are investigated. This interpretation is used for another proof of the existence of Im Hof's hyperbolic Coxeter orthoschemes [see \textit{H.-C. Im Hof}, Expo. Math. 3, 179-186 (1985; Zbl 0572.51012), and Bull. Soc. Math. Belg. Ser. A 42, No. 3, 523-545 (1990)].
Mathematics Subject Classification ID: 52A10
Mathematics Subject Classification ID: 52A55
Mathematics Subject Classification ID: 52B99
zbMATH DE Number: 93783
zbMATH Keywords: space of polygons
zbMATH Keywords: Euclidean plane
zbMATH Keywords: hyperbolic polyhedron
zbMATH Keywords: hyperbolic space
zbMATH Keywords: hyperbolic Coxeter orthoschemes
reviewed by: Bernd Wegner
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 93783