"A pyramid is a polyhedron with one face (known as the "base") a polygon and all the other faces triangles meeting at a common polygon vertex (known as the "apex"). A right pyramid is a pyramid for which the line joining the centroid of the base and the apex is perpendicular to the base. A regular pyramid is a right pyramid whose base is a regular polygon. An n-gonal regular pyramid (denoted ) having equilateral triangles a sides is possible only for n = 3, 4, 5. These correspond to the tetrahedron, square pyramid, and pentagonal pyramid, respectively. " - from Mathworld