Engineering and Technology Journal

Abstract

In this work the basic concept of reflexive polytopeand Gorensteinpolytope and Fano with some theorems about them are given. Three standard binary operations on polytopeswhich are: the cartesian product (×), the direct sum (⊕) and the free join(⋈) are examined. Finally techniques are used to prove the conjecture |V(P)|≤6^(d/2) of the maximal number of vertices for a simplicialreflexive polytopes of even dimension.