Isoperimetric Pentagonal Tilings

Details Isoperimetric Pentagonal Tilings Isoperimetric Pentagonal Tilings

2011-11-26

arxiv.org/abs/1111.6161v1

Mathematics

Metric Geometry

16 pages, 17 figures

Scientific paper

We identify least-perimeter unit-area tilings of the plane by convex
pentagons, namely tilings by Cairo and Prismatic pentagons, find infinitely
many, and prove that they minimize perimeter among tilings by convex polygons
with at most five sides.

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