*Accepted Paper*

**Inserted:** 2 apr 2020

**Last Updated:** 2 apr 2020

**Journal:** Comm. Pure Appl. Math.

**Year:** 2020

**Abstract:**

Let K be a convex polyhedron and F its Wul energy, and let C (K) denote the set of convex polyhedra close to K whose faces are parallel to those of K. We show that, for suciently small , all -minimizers belong to C (K). As a consequence of this result we obtain the following sharp stability inequality for crystalline norms: There exist = (K; n) > 0 and = (K; n) > 0 such that, whenever jEj = jKj and jEKj then F(E)

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