The full symmetry of the cubic system is not realised, however, by a study of the cube alone; we only appreciate it when we come to examine the general form of the cubic system, that which is produced by starting with a face oblique to all three axes, and with different amounts of obliquity to each, and seeing how many repetitions of the face the symmetry demands. The presence of such a face involves as a matter of fact, when all the elements of symmetry are satisfied, the presence also of no less than forty-seven others, symmetrically situated, the forty-eight-sided figure produced being the hexakis octahedron shown in Fig. 21, and which is occasionally actually found developed in nature as the diamond. All diamonds do not by any means exhibit this form so wonderfully rich in faces, but diamonds are from time to time found which do show all the forty-eight faces well developed. [Illustration: FIG. 22.—Measured Crystal of Topaz. ] Besides these four more highly symmetrical systems or styles of crystal architecture, a fifth, the _monoclinic system_, characterised by a single plane of symmetry and one axis of digonal symmetry perpendicular thereto, has already been alluded to, and a typical crystal illustrated in Fig. 15. A sixth, the _rhombic system_, perhaps in some ways the most interesting of all, and certainly so optically, possesses three rectangular axes of symmetry, identical in direction with the crystallographic axes, and three mutually rectangular planes of symmetry, coincident with the axial planes and intersecting each other in the axes. The lengths of the three crystal axes are unequal, however, and herein lies the essential difference from the cube. A very typical rhombic substance is topaz, a crystal of which, about three millimetres in diameter, is shown very much enlarged in Fig. 22. Every face on this crystal has been actually investigated on the goniometer, and the interfacial angles measured. [Illustration: FIG. 23.—Measured Crystal of Copper Sulphate. ] Lastly, there is the seventh, the _triclinic system_, in which there are neither planes nor axes of symmetry, but, even in its holohedral class, only symmetry about the centre, each face having a parallel fellow. Sulphate of copper, blue vitriol, CuSO_{4}.5H_{2}O, shows this type of symmetry, or rather lack of it, very characteristically, and a crystal of this beautiful deep blue salt, measured by the author, is represented in Fig. 23.