  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.
