There is one principal form which is common to both the hexagonal and trigonal systems, namely, the hexagonal prism, and this is the chief form exhibited by quartz crystals. They are terminated by an apparently hexagonal pyramid, but which really consists of a pair of complementary rhombohedra, which are purely trigonal forms; three upper faces of each rhombohedron are developed at one end of the prism which may be regarded as the upper, and the three lower faces of each of the two individual rhombohedra likewise at the lower end of a fully developed doubly terminated crystal. The rhombohedron is the characteristic form of the trigonal system of crystal symmetry, the systematic crystallographic axes being parallel to its edges. It is like a cube deformed by extension or compression along a diagonal, which latter is arranged vertically, and becomes the trigonal axis of symmetry (not a crystallographic axis), as shown in Fig. 70. [Illustration: FIG. 68. ] [Illustration: FIG. 69. Left-handed and Right-handed Crystals of Quartz. ] When two rhombohedra are equally developed, one being rotated with respect to the other 60° round the vertical trigonal axis of symmetry, they together resemble a hexagonal pyramid, and crystals of quartz thus terminated at both ends are not uncommon, so that at first sight a quartz crystal might be mistaken for a hexagonal prism doubly terminated by the hexagonal pyramid, and the mineral considered, in error, to belong to the hexagonal system. [Illustration: FIG. 70.—The Rhombohedron and its Axes. ] But one alternate set of three faces of the hexagonal pyramid at one end, and the oppositely alternate set of three similar faces at the other end, will usually be found to be much less brilliant (indeed often quite dull) than the other alternate three, and very frequently also the amount of development is markedly different, both facts indicating that the terminal faces belong to two different but complementary rhombohedral forms, and that the system of symmetry is the trigonal and not hexagonal. But there is much stronger evidence than this for trigonal symmetry. For the little faces marked _s_ and _x_ on Figs. 68 and 69 are characteristic of the trapezohedral class of the trigonal system, and it will be observed that on one crystal, Fig. 68, these faces occupy and modify a left-hand corner or solid angle on the crystal, while on the other crystal, Fig. 69, they occupy and replace a right-hand solid angle. Now, if a plate be cut out of the former crystal perpendicularly to the axis of the hexagonal prism, that is, to the optic axis of the trigonal uniaxial crystal, it will be found to rotate the plane of polarisation to the left, the direction in which the small faces are situated; while if a similar plate be cut out of the right-handed crystal shown in Fig. 69, that is, one which has the small faces on the right, it will be observed to rotate the plane of polarisation to the right.