pyramid A polyhedron whose one face is a polygon and the other faces are triangles with one common vertex. This polygon is the base of the pyramid. The other triangles are the lateral faces. The common vertex of these lateral faces is the vertex of the pyramid. The segment from the vertex perpendicular to the base is called the altitude of the pyramid. The length of the altitude is called the height of the pyramid. The intersections of the adjacent lateral faces are called the lateral edges of the pyramid.