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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 $(2^{ℝ}2$, dS)$isseparable.Ontheotherhand,wegiveanexampleshowingthat$2ℝ2$isnotseparableinthefundamentalmetricintroducedbyBorsuk.$