Isoperimetric Pentagonal Tilings
  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. 
Ping Ngai Chung, Miguel A. Fernandez, Yifei Li, Michael Mara, Frank   Morgan, Isamar Rosa Plata, Niralee Shah, Luis Sordo Vi...
math.MG