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The purpose of this paper is to compute the minimal fibering degree of anarbitrary projective toric variety. We prove that it equals the lattice widthof the associated polytope. This gives a complete answer to a question asked ina recent paper of Levinson, Ullery and the second author. The minimal fiberingdegree of a polarized projective variety was introduced in that paper in orderto compute the degree of irrationality (a generalization of gonality) of highdegree divisors. From this perspective, our paper gives a higher dimensionalanalogue of results of Kawaguchi and others who computed the gonality of curvesin toric surfaces in terms of lattice widths.

The minimal fibering degree of a toric variety equals the lattice width of its polytope