Modulus and Poincar\'e inequalities on non-self-similar Sierpinski carpets

A carpet is a metric space homeomorphic to the Sierpinski carpet. We characterize, within a certain class of examples, non-self-similar carpets supporting curve families of nontrivial modulus and supporting Poincar'e inequalities. Our results yield new examples of compact doubling metric measure spaces supporting Poincar'e inequalities: these examples have no manifold points, yet embed isometrically as subsets of Euclidean space.