A cone is any three-dimensional shape that tapers from a flat base to a single vertex. A pyramid is a specialized type of cone. Pyramids are cones with polygonal bases. All types of cone are triangles when presented in two dimensions.
In common usage, a pyramid usually refers to a cone with a quadrilateral base. This is due to the fact that pyramids with four sides are the most common type seen in ancient architecture. Egyptian pyramids, Mesopotamian ziggurats, the tombs of Chinese emperors and Aztec temples all utilize this type of pyramidal architecture.
In mathematics a pyramid refers to any cone with a polygonal base. Some pyramids have more specific names. For example, a pyramid with a triangular base is specifically referred to as a tetrahedron. In projective geometry, a cylinder is also classified as a cone, though not a pyramid. It has a round base, and in this form of geometry it is assumed to have an apex at infinity.
Different formulas are used to calculate the area and volume of pyramids and circular cones due to the cone's circular base. All pyramids use the same formula to calculate these measurements, regardless of the shape of the base and the number of sides.