A cubical polytope is a convex polytope of which very facet is a combinatorial cube. We ask for the numbers which occur as vertex numbers of d-dimensional cubical polytopes, and we show, as a first step, that every cubical d-polytope for even d > 4 has an even number of vertices.

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A cubical polytope is a convex polytope of which every facet is a combinatorial cube. We give here a complete enumeration of all the cubical d-polytopes with fewer than 2 a+ 1 vertices, for d > 4. 322 G. Blind and R. Blind

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