1. A method of detecting collision between at least one first numerically-simulated polyhedral object ( 10 ) and at least one second numerically-simulated polyhedral object ( 20 ) and of constructing geometrical information about proximity and contact between them; the method being characterized in that the first and second numerically-simulated polyhedral objects ( 10 , 20 ) are represented in the form of simplicial complexes (K 1 , K 2 ) in R n , where R n designates the Cartesian product of the body of real numbers multiplied by itself n times, with n equal to 2 or 3; wherein a pre-processing step is carried out for each simplicial complex (K) for which the coordinates of the vertices are given in a fixed system of coordinates; wherein the pre-processing step consists at least in calculating for each face (σ) of each simplicial complex (K) a geometrical description of the polyhedral cone corresponding to the normals in the strong sense (n |K| (Int σ)) associated with that face (σ), determining the label of the contact class to which that face (σ) belongs, and determining for each simplicial complex (K) a tree of encompassing volumes of the object of the simplicial complex (K) from both the position of the faces (σ) of the simplicial complex (K) and the sets of associated normals in the strong sense (n|K| (σ)); and wherein, from information obtained after the pre-processing step, a step of calculating local minimum distances (LMD) and quasi local minimum distances (quasi-LMD), each quasi local minimum distance corresponding to a pair of points belonging to respective distinct objects and that would define a local minimum distance (LMD) if the position of one object relative to the other were subject to a rotation by a small angle (γ max ) below a given threshold.