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We define a metric d S , called the shape metric, on the hyperspace 2 X of all non-empty compact subsets of a metric space X. Using it we prove that a compactum X in the Hilbert cube is movable if and only if X is the limit of a sequence of polyhedra in the shape metric. This fact is applied to show that the hyperspace (2 R 2 , d S ) is separable. On the other hand, we give an example showing that 2 R 2 is not separable in the fundamental metric introduced by Borsuk.1. The shape metric. Let H denote the Hilbert space of all square summable sequences of real numbers. If X is a subset of H we denote by

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