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We prove that every finite-volume hyperbolic 3-manifold M with p > 0 cuspsadmits a canonical, complete, piecewise Euclidean CAT(0) metric, with acanonical projection to a CAT(0) spine K. Moreover, (a) the universal cover ofM endowed with the CAT(0) metric is a union of Euclidean half-spaces, gluedtogether by identifying Euclidean polygons in their bounding planes by pairwiseisometry (b)each cusp of M in the CAT(0) metric is a non-singular metricproduct of a (Euclidean) cusp torus and a half-line (c) all metricsingularities are concentrated on the 1-skeleton of K, with cone angles amultiple of pi (d) there is a canonical deformation of the hyperbolic metricwith limit the CAT(0) piecewise Euclidean metric. The proof uses Ford domains;the construction is essentially the polar-dual of the Epstein-Penner canonicaldecomposition, and generalizes to higher dimension.

Cusped hyperbolic 3-manifolds: canonically CAT(0) with CAT(0) spines