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Metric Combinatorics of Convex Polyhedra: Cut Loci and Nonoverlapping Unfoldings

2008
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Discrete & Computational Geometry
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Let S be the boundary of a convex polytope of dimension d + 1, or more generally let S be a convex polyhedral pseudomanifold. We prove that S has a polyhedral nonoverlapping unfolding into R d , so the metric space S is obtained from a closed (usually nonconvex) polyhedral ball in R d by identifying pairs of boundary faces isometrically. Our existence proof exploits geodesic flow away from a source point v ∈ S, which is the exponential map to S from the tangent space at v. We characterize the

doi:10.1007/s00454-008-9052-3
fatcat:ltrez2irufgupiq63mrjxc4tym