Über regulär pflasterbare konvexe Polygone. (On regular tilings of convex polygons)
type: Item
instance of: scholarly article
title: Über regulär pflasterbare konvexe Polygone. (On regular tilings of convex polygons)
zbMATH Open document ID: 0624.52008
author: Eckhard Wildgrube
published in: Beiträge zur Algebra und Geometrie
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/138387
review text: The author considers tiling a convex n-gon edge-to-edge with regular polygons of edge length one in an Euclidean plane. If such a tiling is possible, the n-gon is called regular decomposible. \textit{J. Malkevitch} [Ann. N. Y. Acad. Sci. 440, 299-303 (1985; Zbl 0575.52007)] showed that for and only for every natural number n with \(3\leq n\leq 12\) there exists a convex n-gon which is regular decomposible into regular triangles and quadrangles. Now allowing all regular p-gons with edge length one the author proves two assertions: (1) For a regular decomposible convex n-gon (not regular with edge length 1, that means non-trivial regular decomposible) also holds \(3\leq n\leq 12\). (2) The tiles of such a tiling can only be regular p-gons with \(p=3,4,5,6\), or 12. - Because regular 6- gons and 12-gons can be dissected into regular triangles and quadrangles the set of regular triangles, quadrangles, and pentagons of edge length one is a generator set for all non-trivial regular decomposible polygons. - These results were elementary found by using the assumption that the polygons are convex and by using estimations for the angle sums at the vertices.
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 52A10
zbMATH DE Number: 4013438
zbMATH Keywords: convex polygons
zbMATH Keywords: tiling with regular polygons
zbMATH Keywords: regular decomposible
reviewed by: Johannes Böhm
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4013438