While all of the infernal names are said to reside in the Royal Palace of Hell, four are set apart as being particularly powerful. These are known to LaVeyan Satanists as the crown princes of Hell.
Each prince is associated with a cardinal direction: north, south, east and west. This is in line with other Western magical practices that commonly associate supernatural beings with the cardinal points.
Specifically, ceremonial magic has commonly ascribed the four Biblical archangels – Michael, Raphael, Uriel, and Gabriel – to the four directions for several hundred years.
In the "Satanic Bible," Anton LaVey also associates each prince with one of the four physical elements: fire, earth, air and water. This is again a common practice in Western magical traditions.
Satan
Satan is a Hebrew term meaning "adversary." Unlike the common Christian view of Satan as opposing the will of God, in his original context, Satan was a servant of God. He tested the faith of God's followers by being adversarial toward them, tempting them to stray from God's path or denounce him in their moments of misery.
For Satanists, he is:
The adversary of: mundanity, mediocrity, right hand path, stupidity, conformity for the sake of conformity, self destruction, religion, gods (" The Aspect of Satan," Vexen Crabtree)
He is associated in the Satanic Bible with the element of fire and the south.