The boundary characteristic and Pick's theorem in the Archimedean planar tilings
type: Item
instance of: scholarly article
title: The boundary characteristic and Pick's theorem in the Archimedean planar tilings
zbMATH Open document ID: 0634.52010
DOI: 10.1016/0097-3165(87)90063-X
author: Ding Ren
author: John R. Reay
published in: Journal of Combinatorial Theory. Series A
publication date: 1987-01-01T00:00:00Z
review text: Pick's theorem, giving the area of a lattice polygon by the number of lattice points on its boundary and in its interior, is generalized to certain polygons whose vertices are among the vertices of one of the 11 Archimedean tilings of the plane. For this purpose two combinatorial characteristics of the polygon are introduced in addition to its Pick number, its boundary and adjacency characteristic. The proofs mainly work by shelling appropriate dissections of the polygon.
Mathematics Subject Classification ID: 52C07
zbMATH DE Number: 4032506
zbMATH Keywords: Pick's theorem
zbMATH Keywords: Archimedean tilings
Wikidata QID: Q56029316
reviewed by: Christoph Schulz
MaRDI profile type: Publication
cites work: Q3273607
cites work: From Euler's Formula to Pick's Formula Using an Edge Theorem
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cites work: Tilings by Regular Polygons
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cites work: On the Volume of Lattice Polyhedra
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cites work: An Inequality for Convex Lattice Polygons
full work available at URL: 0097-3165(87)90063-x
OpenAlex ID: W2064022936
description: scientific article; zbMATH DE number 4032506