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We describe an algorithm to compute the geodesics in an arbitrary CAT(0)cubical complex. A key tool is a correspondence between cubical complexes ofglobal non-positive curvature and posets with inconsistent pairs. Thiscorrespondence also gives an explicit realization of such a complex as thestate complex of a reconfigurable system, and a way to embed any interval inthe integer lattice cubing of its dimension.

Geodesics in CAT(0) Cubical Complexes