A parallelepiped whose six faces are all squares. The cube (see illus.) is one of the five regular solids known to the ancient Greeks, who proposed the famous problem (now proved to be unsolvable) of constructing, with the use of the compass and unmarked straightedge alone, a cube whose volume is twice that of a given cube. The edge of the desired cube may be found by use of conic sections. A cube has eight vertices and twelve edges. Each vertex is on three edges and three faces, each edge is on two vertices and two faces, and each plane is on four vertices and four edges.