longest diagonal of a cube) of a pure (i.e., type IIa) diamond has a hardness value of when scratched with a nanodiamond tip, while the nanodiamond sample itself has a value of when tested with another nanodiamond tip. Because the test only works properly with a tip made of harder material than the sample being tested, the true value for nanodiamond is likely somewhat lower than . The precise tensile strength of diamond is unknown, though strength up to has been observed, and theoretically it could be as high as depending on the sample volume/size, the perfection of diamond lattice and on its orientation: Tensile strength is the highest for the [100] crystal direction (normal to the cubic face), smaller for the [110] and the smallest for the [111] axis (along the longest cube diagonal). Diamond also has one of the smallest compressibilities of any material. Cubic diamonds have a perfect and easy octahedral cleavage, which means that they only have four planes—weak directions following the faces of the octahedron where there are fewer bonds—along which diamond can easily split upon blunt impact to leave a smooth surface. Similarly, diamond's hardness is markedly directional: the hardest direction is the diagonal on the cube face, 100 times harder than the softest direction, which is the dodecahedral plane. The octahedral plane is intermediate between the two extremes. The diamond cutting process relies heavily on this directional hardness, as without it a diamond would be nearly impossible to fashion. Cleavage also plays a helpful role, especially in large stones where the cutter wishes to remove flawed material or to produce more than one stone from the same piece of rough (e.g. Cullinan Diamond). Diamonds crystallize in the diamond cubic crystal system (space group Fdm) and consist of tetrahedrally, covalently bonded carbon atoms. A second form called lonsdaleite, with hexagonal symmetry, has also been found, but it is extremely rare and forms only in meteorites or in laboratory synthesis. The local environment of each atom is identical in the two structures. From theoretical considerations, lonsdaleite is expected to be harder than diamond, but the size and quality of the available stones are insufficient to test this hypothesis. In terms of crystal habit, diamonds occur most often as euhedral (well-formed) or rounded octahedra and twinned, flattened octahedra with a triangular outline. Other forms include dodecahedra and (rarely) cubes. There is evidence that nitrogen impurities play