A pyramid has a polygonal base and a point above the center of the polygon; a dipyramid has two points on either side of the polygon. A prism is formed by joining the sides of two parallel polygons so that the vertical sides are quadrilaterals. In an antiprism, the parallel polygons are slightly twisted from each other, and the vertical sides are triangles.

Gyroelongated dipyramids, represented here as sets of tetrahedra, are an infinite family of polyhedra constructed by separating a dipyramid and inserting an antiprism between its top and bottom halves. One of the five Platonic solids, the icosahedron, belongs to this family of polyhedra. These shapes could be used in architecture—for example, for roofs.