"The reason polytheisim is illogical is because it self contradicts. On the one hand it declares many Gods while on the other it declares a body working as one. If theism is to exist it must be one all powerful God. If there are multiple God's, either one has to reign supreme which results in there being one God or all have to work together like the cells in the human body, which results in one God. So, polytheism is either describing many gods acting as one or many gods ruled by one."
So how do explain the trinity? And how does Satan fit into this mix?
And how does Satan fit into this mix?
I. THE DOGMA OF THE TRINITY The Trinity is the term employed to signify the central doctrine of the Christian religion -- the truth that in the unity of the Godhead there are Three Persons, the Father, the Son, and the Holy Spirit, these Three Persons being truly distinct one from another. Thus, in the words of the Athanasian Creed: "the Father is God, the Son is God, and the Holy Spirit is God, and yet there are not three Gods but one God." In this Trinity of Persons the Son is begotten of the Father by an eternal generation, and the Holy Spirit proceeds by an eternal procession from the Father and the Son. Yet, notwithstanding this difference as to origin, the Persons are co-eternal and co-equal: all alike are uncreated and omnipotent. This, the Church teaches, is the revelation regarding God's nature which Jesus Christ, the Son of God, came upon earth to deliver to the world: and which she proposes to man as the foundation of her whole dogmatic system.
source http://www.newadvent.org/cathen/15047a.htm
And how does Satan fit into this mix?
I assume you raised this question because you assume satan is co-equal with God. He is not. He was created by God with all the other angels. Just as man denies God's sovereignty, so to did satan.