2Dep. of Mathematics, American University of the Middle East, KUWAIT
In this paper, we introduce the notion of crossed polysquare of polygroups and we give some of its properties. Our results extend the classical results of crossed squares to crossed polysquares. One of the main tools in the study to polygroups is the fundamental relations. These relations connect polygroups to groups, and on the other hand, introduce new important classes. So, we consider a crossed polysquare and by using the concept of fundamental relation, we obtain a crossed square.