Published online by Cambridge University Press: 26 February 2010
The object of the present note is to prove the following theorem. †
Theorem. Let P be a convex d-polytope in d-dimensional real vector space Rd (d ≥ 2). If each d-polytope which is the intersection of two translates of P has the same number of vertices as P, then P is a direct linear sum ‡ of simplices.