Perfect Prismatoids and the Conjecture Concerning Face Numbers of Centrally Symmetric Polytopes

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

• многогранники
• многогранники Ханнера
• гипотеза Калаи