INERALOGY 365 Tetra gonal twins. It is seen in fig. 168 of blende, where the two parts of the rhombic dodecahedron are united by it. Magnetite, spinel, and diamond Fig. 167. Fig. 168. frequently occur in octahedral hemitropes of the same composition (fig. 169). This is also the face of composition for tetartohedral hemitropes. Fig. 170 is that of the diamond. Here six of the faces of the six- Fig. 169. Fig. 170. faced octahedron, with six faces diagonally opposite, form a low double six-sided pyramid (a portion of an octahedral face truncating each) through an 180 revolution of one set of these. Garnet some times shows both twins and hemitropes of the dodecahedron, of dodecahedral composition. In the tetragonal system, twin crystals are very uncommon, but hemitropes frequent. With parallel axes they very seldom occur, but are seen in chalcopyrite. When the axes are inclined, the plane of union is usually one of the faces of the primary pyramid ; and, as these faces are all similar, composition may take place simultaneously parallel to all. Very complicated forms hence result, as seen in chalcopyrite and in cassiterite (fig. 171)- Fig. 171 Fig. 172. In cassiterite the plane of union is frequently one of the faces of the pyramid Poo , sometimes one of those faces that replace the polar edges of P (figs. 172 173). From the bend the latter form is termed geniculated. Hexa gonal twins. Fig. 173. Fig. 174. Hausmannite occurs in hemitropes of the primary P ; and on the polar edges of this other twins are symmetrically repeated, a central individual appearing like a support to the others (figs. 174, 175). In the hexagonal system twins are very common among the rhombohedral (the hemihedral) and the tetartohedral forms; while hemitropes prevail among the hexagonal or holohedral forms. The twins are generally formed by the interpenetration of two rhombo- hedrons, a + and a - , the vertical axis being the axis of composi tion; as in chabasite (fig. 176), cinnabar, levyne, calcite, &c. Some times six or more crystals, united parallel to the prismatic planes, Fig. 175. Fig. 176. form rosettes; as in chabasite from Giant s Causeway. The almost endless stellate forms of crystals of snow are built up in this manner. Many of the most beautiful combinations to be seen among crystals result from this mode of arrangement. Parallel groupings of hexagonal prisms also occur, as in apatite (fig. 177). Rock crystal, in consequence of the tetartohedral character of its crystallization, exhibits twins in which the double hexagonal pyramid P may be said to be separated into two rhombohedrons P and r; these, though geometrically similar, are physi- Fig. 177. Fig. 178. cally distinct. In fig. 1 78 the two individuals have not entirely in terpenetrated, and might be regarded as simply grown together with parallel axes; but in fig. 147 there is so complete an inter- penetration that the composite character of the crystal is only evi denced through a difference in the character of the surfaces of the two halves, which are most irregularly disposed. The hemitropes of this system often form regular crystals, when the two halves have been united by a plane parallel to the base, so as to appear like a simple crystal, as in fig. 179. Here each end shows the forms o>R, - |R ( but the terminal faces appear in parallel instead of alternate posi tion. Something of the same is seen in fig. 180, a hemitrope scalenohedron from Derbyshire. Hemitropes with the face of the primitive rhombohedron as the face of composition are also com mon ; and they are sometimes joined by a face of - R, the two axes forming an angle of 127 34 . Occasionally a third individual is interposed in a lamellar form, as in fig. 181, where the faces of the two outer portions become parallel. This is found in some pieces of Iceland spar. When the crystals unite in a face of the primary rhombohedron, they form an angle of 89 8 ; hemitropes on this law are easily recognized by their differing so little from a right angle in the re-entering bend (figs. 182, 183). The faces which in this species act as faces of composition are exceedingly numerous ; other examples are figs. 142, 146, 148, and 149. In the rir/ht prismatic system twin crystals with parallel axes are Right rare, but with oblique axes common, the faces of union being one of prismatic
the faces of the prism ooP. Twins of this kind occur frequently in twins.