Mathematical Proceedings of the Cambridge Philosophical Society

A note on tilings and strong isoperimetric inequality

a1 Dipartimento di Matematica, Università di Milano, Via Saldini 50, 20133 Milano, Italia


We show that the edge graph of a locally finite tiling in the plane satisfies a strong isoperimetric inequality if one among the lower averages of what we call the characteristic numbers of edges, vertices and tiles is positive.

(Received May 31 1996)
(Revised November 22 1996)