The longest perimeter small triacontadigon
Bernd Mulansky, Andreas Potschka
TL;DR
This paper presents a convex 32-gon with unit diameter that has the longest known perimeter, improving previous examples and contributing to geometric optimization knowledge.
Contribution
It introduces the first known small triacontadigon with a perimeter longer than all previously documented convex 32-gons of unit diameter.
Findings
Longest known perimeter for a small triacontadigon
Perimeter value: 3.1403311569546
Advances geometric optimization of convex polygons
Abstract
We showcase a small triacontadigon, i.e. a convex -gon of unit diameter, with perimeter , which improves on all examples available so far.
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Taxonomy
TopicsGeometric and Algebraic Topology · Supramolecular Self-Assembly in Materials · Point processes and geometric inequalities