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Different sub-fields of math use different definitions of "face". According to one definition commonly applied to convex polyhedra, a spherical ball in n dimensions has one face of dimension n (the entire ball), an uncountably infinite number of faces of dimension 0 (each point on the surface), and one face of dimension -1 (the empty set). In particular, there are no facets (faces of dimension n-1). But that's only one definition.
