The boundary characteristic and Pick's theorem in the Archimedean planar tilings

DOI10.1016/0097-3165(87)90063-XzbMath0634.52010OpenAlexW2064022936WikidataQ56029316 ScholiaQ56029316MaRDI QIDQ1096892

John R. Reay, Ding Ren

Publication date: 1987

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0097-3165(87)90063-x

zbMATH Keywords

Archimedean tilingsPick's theorem

Mathematics Subject Classification ID

Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07)

Related Items (13)

Thin Hamiltonian cycles on Archimedean graphs ⋮ A new Pick-type theorem on the hexagonal lattice ⋮ Word-representability of face subdivisions of triangular grid graphs ⋮ Realizable quadruples for hex-polygons. Combinatorics of honeycombs ⋮ A new formula for the volume of lattice polyhedra ⋮ Area-Optimal Simple Polygonalizations: The CG Challenge 2019 ⋮ Areas of lattice figures in the planar tilings with congruent regular polygons ⋮ Polynomials and spatial Pick-type theorems ⋮ Primitive and mensurable hex-triangles ⋮ The boundary characteristic and the volume of lattice polyhedra ⋮ A note on discrete lattice-periodic sets with an application to Archimedean tilings ⋮ A note on area of lattice polygons in an Archimedean tiling ⋮ Perfect colorings of multipatterns in the plane

Cites Work

• On the Volume of Lattice Polyhedra
• An Inequality for Convex Lattice Polygons
• Lattice Points and Pick's Theorem
• Calculating Surface Areas from a Blueprint
• Triangulations and Pick's Theorem
• Tilings by Regular Polygons
• From Euler's Formula to Pick's Formula Using an Edge Theorem
• Lattice Points and Polygonal Area
• Unnamed Item

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