The cyclic polytope attains the maximum number of vertices in a hyperplane slice, and the paper determines the missing vertex counts, or gaps, for slices of hypercubes up to dimension seven.
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On the Number of Vertices in a Hyperplane Section of a Polytope
The cyclic polytope attains the maximum number of vertices in a hyperplane slice, and the paper determines the missing vertex counts, or gaps, for slices of hypercubes up to dimension seven.