An octagonal pyramid has nine faces: eight are triangular faces and one face is a regular octagon. It also has 23 edges and nine vertices. The topmost corner that connects all the faces is called the apex.
Any pyramid whose regular polygonal base has n sides will have n+1 faces, 2n edges and n+1 vertex. The volume of an octagonal pyramid is calculated by (b*h) / 3 where b is the base area of the pyramid and h is the vertical height of the pyramid (from the center of the base to the apex). The surface area is calculated by simply adding the base area to the lateral area (area of the eight triangular faces).
There are several other types of pyramids, and each is named after the shape of its base. If the apex is located directly above the center of the base, the pyramid is referred to as a right pyramid, and if the apex is located anywhere else, it is an oblique pyramid. The faces of an oblique pyramid are not congruent. Any pyramid whose base is not a regular polygon is referred to as an irregular pyramid. Whenever the shape of the polygonal base of a pyramid is not mentioned, it is typically assumed to be a square pyramid. All pyramids are a subclass of prismatoids.