The volume of any tetrahedron that shares three converging edges of a parallelepiped is equal to one sixth of the volume of that parallelepiped (see proof). Surface area The surface area of a parallelepiped is the sum of the areas of the bounding parallelograms: (For labeling: see previous section.) Special cases by symmetry The parallelepiped with Oh symmetry is known as a cube, which has six congruent square faces. The parallelepiped with D4h symmetry is known as a square cuboid, which has two square faces and four congruent rectangular faces. The parallelepiped with D3d symmetry is known as a trigonal trapezohedron, which has six congruent rhombic faces (also called an isohedral rhombohedron). For parallelepipeds with D2h symmetry, there are two cases: Rectangular cuboid: it has six rectangular faces (also called a rectangular parallelepiped, or sometimes simply a cuboid). Right rhombic prism: it has two rhombic faces and four congruent rectangular faces. Note: the fully rhombic special case, with two rhombic faces and four congruent square faces , has the same name, and the same symmetry group (D2h , order 8). For parallelepipeds with C2h symmetry, there are two cases: Right parallelogrammic prism: it has four rectangular faces and two parallelogrammic faces. Oblique rhombic prism: it has two rhombic faces, while of the other faces, two adjacent ones are equal and the other two also (the two pairs are each other's mirror image). Perfect parallelepiped A perfect parallelepiped is a parallelepiped with integer-length edges, face diagonals, and space diagonals. In 2009, dozens of perfect parallelepipeds were shown to exist, answering an open question of Richard Guy. One example has edges 271, 106, and 103, minor face diagonals 101, 266, and 255, major face diagonals 183, 312, and 323, and space diagonals 374, 300, 278, and 272. Some perfect parallelepipeds having two rectangular faces are known. But it is not known whether there exist any with all faces rectangular; such a case would be called a perfect cuboid. Parallelotope Coxeter called the generalization of a parallelepiped in higher dimensions a parallelotope. In modern literature, the term parallelepiped is often used in higher (or arbitrary finite) dimensions as well. Specifically in n-dimensional space it is called n-dimensional parallelotope, or simply -parallelotope (or -parallelepiped). Thus a parallelogram is a 2-parallelotope and a parallelepiped is a 3-parallelotope. More generally a parallelotope, or voronoi parallelotope, has parallel and congruent opposite facets. So a 2-parallelotope is a