Vol. 7, No. 4, 2014

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Perimeter-minimizing pentagonal tilings

Ping Ngai Chung, Miguel A. Fernandez, Niralee Shah, Luis Sordo Vieira and Elena Wikner

Vol. 7 (2014), No. 4, 453–478
Abstract

We provide examples of perimeter-minimizing tilings of the plane by convex pentagons and examples of perimeter-minimizing tilings of certain small flat tori.

Keywords
tilings, pentagon, isoperimetric
Mathematical Subject Classification 2010
Primary: 52C20
Secondary: 52C05
Milestones
Received: 29 March 2012
Accepted: 26 May 2012
Published: 31 May 2014

Communicated by Michael Dorff
Authors
Ping Ngai Chung
Department of Mathematics
Massachusetts Institute of Technology
305 Memorial Drive
Cambridge, MA 02139
United States
Miguel A. Fernandez
Mathematics and Computer Science Department
Truman State University
100 E. Normal Avenue
Kirksville, MO 63501
United States
Niralee Shah
Department of Mathematics and Statistics
Bronfman Science Center
Williams College
Williamstown, MA 01267
United States
Luis Sordo Vieira
Department of Mathematics
Wayne State University
656 W. Kirby
Detroit, MI 48202
United States
Elena Wikner
Department of Mathematics and Statistics
Bronfman Science Center
Williams College
Williamstown, MA 01267
United States