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.
Combinatorics of sections of polyt opes and Coxeter groups in Lobachevsky spaces
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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.