Abstract:
In this paper we introduce and study a class of centrally symmetric polytopes — perfect prismatoids — and some its properties related to the famous conjecture concerning face numbers of centrally symmetric polytopes are proved. It is proved that any Hanner polytope is a perfect prismatoid and any perfect prismatoid is affine equivalent to some $0/1$-polytope.
Keywords:polytopes, Hanner polytopes, Kalai's conjecture.