Enumerating isodiametric and isoperimetric polygons

DOI10.1016/j.jcta.2011.03.004zbMath1230.52013OpenAlexW2088620080MaRDI QIDQ543911

Michael J. Mossinghoff

Publication date: 17 June 2011

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

Full work available at URL: https://doi.org/10.1016/j.jcta.2011.03.004

zbMATH Keywords

widthpolygondiameterisoperimetric problemperimeterisodiametric problemdihedral compositionisoplatometric problem

Mathematics Subject Classification ID

Computational aspects related to convexity (52B55) Inequalities and extremum problems involving convexity in convex geometry (52A40) Isoperimetric problems for polytopes (52B60) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (8)

Extremal problems for spherical convex polygons ⋮ Maximal perimeter, diameter and area of equilateral unit-width convex polygons ⋮ Tight bounds on the maximal perimeter of convex equilateral small polygons ⋮ The equilateral small octagon of maximal width ⋮ Sporadic Reinhardt polygons ⋮ The small octagons of maximal width ⋮ Most Reinhardt polygons are sporadic ⋮ Tight bounds on the maximal perimeter and the maximal width of convex small polygons

Cites Work

• A discrete isoperimetric problem
• The small octagon with longest perimeter
• Isoperimetric polygons of maximum width
• The largest small hexagon
• The largest small octagon
• The minimum diameter octagon with unit-length sides: Vincze's wife's octagon is suboptimal
• On convex polygons of maximal width
• Diameter graphs of polygons and the proof of a conjecture of Graham
• Extremal problems for convex polygons
• Isodiametric problems for polygons
• A $1 Problem
• The Isoperimetric Problem
• A note on the cyclotomic polynomial
• The Kakeya Problem
• Über das Kreisteilungspolynom
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