An algorithm for classification of fundamental polygons for a plane discontinuous group
type: Item
instance of: scholarly article
title: An algorithm for classification of fundamental polygons for a plane discontinuous group
zbMATH Open document ID: 1416.52012
DOI: 10.1007/978-3-319-78434-2_14
author: Zoran Lučić
author: Emil Molnár
author: Nebojša Vasiljević
publication date: 2019-04-30T00:00:00Z
review text: An algorithm and the computer program for complete enumeration of combinatorial equivalence classes of fundamental polygons for any fixed plane discontinuous group is given. This result is due to Delone for the Euclidean plane but for hyperbolic plane it is a long standing problem. \par Some nontrivial bounds on the number of vertices and edges of the fundamental polygon of the plane discontinuous group in the term of its Macbeath signature is given. \par For some concrete groups a full lists of its fundamental polygons are obtained. For the entire collection see [Zbl 1400.52002].
reviewed by: Anton Shutov
Mathematics Subject Classification ID: 52C20
Mathematics Subject Classification ID: 57S30
Mathematics Subject Classification ID: 51M10
Mathematics Subject Classification ID: 68R99
zbMATH DE Number: 7049370
zbMATH Keywords: plane discontinuous group
zbMATH Keywords: fundamental polygon
zbMATH Keywords: Macbeath signature
zbMATH Keywords: Poincaré-Delone problem
MaRDI profile type: Publication
full work available at URL: 978-3-319-78434-2 14
OpenAlex ID: W2808159397
description: scientific article; zbMATH DE number 7049370