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This paper is concerned with the computation of the skeleton of a shape Ω included in 驴2. We show some connections between the Euclidean distance function d to 驴Ω and the solution u of the Poisson problem Δu(x)=驴1 if x is in Ω and u(x)=0 if x is on 驴Ω. This enables us to propose a new and fast algorithm to compute an approximation of the skeleton of 驴Ω. We illustrate the approach with some numerical experiments.