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Updated: Aug 9, 2026

Applying Permanent, Robust Stenciled Patterns of Fine Particles to Elastomeric Surfaces
Published on: July 8, 2025
Tessellation of a stripe
Piotr Garstecki1, George M Whitesides
1Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA. garst@ichf.edu.pl
Abstract:
This paper describes enumeration of a class of topologically distinct periodic divisions of a stripe. Optimization of the geometry of these periodic tilings--optimization that yields minimum total perimeter of the tiles--gives a set of physically plausible periodic structures of monodisperse, two-dimensional foams bounded by two parallel walls. Evaluation of the minimum total perimeters of the lattices that we enumerated suggests two possible lower bounds for the mean perimeter of tiles forming periodic coverings of a stripe.
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