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These facets are themselves polytopes, whose facets are (n - 2)-dimensional ridges of the original polytope. Every ridge arises as the intersection of two facets (but the intersection of two facets need not be a ridge). Ridges are once again polytopes whose facets give rise to (n - 3)-dimensional boundaries of the original polytope, and so on. These bounding sub-polytopes may be referred to as faces, or specifically j-dimensional faces

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