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The aim of this paper is to show that the supercover of an m-flat (i.e. a Euclidean affine subspace of dimension m) in Euclidean n-space is a discrete analytical object. The supercover of a Euclidean object F is a discrete object consisting of all the voxels that intersect F. A discrete analytical object is a set of discrete points that is defined by a finite set of inequalities. A method to determine the inequalities defining the supercover of an m-flat is provided.