English

Isoperimetric Pentagonal Tilings

Metric Geometry 2011-11-29 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1111.6161,
  title  = {Isoperimetric Pentagonal Tilings},
  author = {Ping Ngai Chung and Miguel A. Fernandez and Yifei Li and Michael Mara and Frank Morgan and Isamar Rosa Plata and Niralee Shah and Luis Sordo Vieira and Elena Wikner},
  journal= {arXiv preprint arXiv:1111.6161},
  year   = {2011}
}

Comments

16 pages, 17 figures

R2 v1 2026-06-21T19:41:54.590Z