Inner Diagonals of Convex Polytopes

An inner diagonal of a polytope P is a segment that joins two vertices of P and that lies, except for its ends, in P's relative interior. The paper's main results are as follows: (a) Among all d-polytopes P having a given number v of vertices, the maximum number of inner diagonals is [[formula]]−dv+[[formula]]; when d⩾4 it is attained if and only if P is a stacked polytope. (b) Among all d-polytopes having a given number f of facets, the …