The Great Pyramids of Egypt are square pyramids. Their base is in the shape of a square, and the apex is centered on top.
Triangular pyramids, instead of having a square base, have a triangular base. A pentagonal pyramid has a pentagon as its base. This rule applies to many other shapes.
Pyramids can vary based on where the apex lies in relation to the base. The apex is the point where all of the sides meet at the top of the pyramid. In a right pyramid, the apex lies directly above the center point of the base, but in an oblique pyramid, the apex can be off to the side, giving the pyramid an uneven look.
Regular and irregular pyramids exist. Regular pyramids have a regular polygon, such as a square, as the base. Irregular pyramids have an irregular polygon as the base.