The different types of pyramids are named after the shape of their polygonal base. For example, a pyramid with an octagon shaped base will be an octagonal pyramid. When the shape of the base is not specified, it is typically assumed to be a square. A pyramid with a triangular base is generally referred to as a tetrahedron.

A pyramid whose apex is located directly above the center of the base are known as right pyramids, while the opposite is called an oblique pyramid. If the base of the pyramid is not a regular polygon, it's called an irregular pyramid; otherwise it's a regular pyramid.

The volume of all pyramids is given by (b*h)/3, where b is the base area and h is the height from the center of the base to the apex. The total surface area of any pyramid is the total sum of the surface areas of each face. Aside from the base, all the faces of a pyramid are triangles. If it is a regular pyramid, all the triangles are isosceles and congruent.