Tessellation of a stripe

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.