Hexagonal bipyramid of the second order, bounded by twelve faces (s in figs. 79 and 80); indices {1121}, {1122} ... {h.h.2h.l }.
Dihexagonal prism, consisting of twelve faces parallel to the hexad axis and inclined to the vertical planes of symmetry; indices {hiko}.
Hexagonal prism of the first order {1010}, consisting of six faces parallel to the hexad axis and perpendicular to one set of three vertical planes of symmetry (m in figs. 71, 78-80).
Hexagonal prism of the second order {1120}, consisting of six faces also parallel to the hexad axis, but perpendicular to the other set of three vertical planes of symmetry (a in fig. 78).
Basal pinacoid {0001}, consisting of a pair of parallel planes perpendicular to the hexad axis (c in figs. 71, 78-80).
Beryl (emerald), connellite, zinc, magnesium and beryllium crystallize in this class.
Bipyramidal Class
Here there is a plane of symmetry perpendicular to the hexad axis; there is also a centre of symmetry. All the closed forms are hexagonal bipyramids; the open forms are hexagonal prisms or the basal pinacoid. The general form {hikl} is hemihedral with parallel faces with respect to the general form of the holosymmetric class.
Apatite (q.v.), pyromorphite, mimetite and vanadinite possess this degree of symmetry.
Dihexagonal Pyramidal Class
Six planes of symmetry of two kinds intersect in the hexad axis. The hexad axis is uniterminal and all the forms are open forms. The general form {hikl} consists of twelve faces at one end of the crystal, and is a dihexagonal pyramid. The hexagonal pyramids {hohl} and (h.h.2h.l) each consist of six faces at one end of the crystal. The prisms are geometrically the same as in the holosymmetric class. Perpendicular to the hexad axis are the pedions (0001) and (0001).
Iodyrite (AgI), greenockite (CdS), wurtzite (ZnS) and zincite (ZnO) are often placed in this class, but they more probably belong to the hemimorphic-hemihedral class of the rhombohedral division of this system.
Trapezohedral Class
Six dyad axes of two kinds are perpendicular to the hexad axis. The general form {hikl} is the hexagonal trapezohedron bounded by twelve trapezoidal faces. The other simple forms are geometrically the same as in the holosymmetric class. Barium-anti-monyldextro-tartrate + potassium nitrate (Ba(SbO)2(C4H4O6)2·KNO3) and the corresponding lead salt crystallize in this class.
Hexagonal Pyramidal Class
No other element is here associated with the hexad axis, which is uniterminal. The pyramids all consist of six faces at one end of the crystal, and prisms are all hexagonal prisms; perpendicular to the hexad axis are the pedions.
Lithium potassium sulphate, strontium-antimonyl dextro-tartrate, and lead-antimonyl dextro-tartrate are examples of this type of symmetry. The mineral nepheline is placed in this class because of the absence of symmetry in the etched figures on the prism faces (fig. 92).
(g) Regular Grouping of Crystals.
Crystals of the same kind when occurring together may sometimes be grouped in parallel position and so give rise to special structures, of which the dendritic (from δένδρον, a tree) or branch-like aggregations of native copper or of magnetite and the fibrous structures of many minerals furnish examples. Sometimes, owing to changes in the surrounding conditions, the crystal may continue its growth with a different external form or colour, e.g. sceptre-quartz.
Regular intergrowths of crystals of totally different substances such as staurolite with cyanite, rutile with haematite, blende with chalcopyrite, calcite with sodium nitrate, are not uncommon. In these cases certain planes and edges of the two crystals are parallel. (See O. Mügge, “Die regelmässigen Verwachsungen von Mineralien verschiedener Art,” Neues Jahrbuch für Mineralogie, 1903, vol. xvi. pp. 335–475).
But by far the most important kind of regular conjunction of crystals is that known as “twinning.” Here two crystals or individuals of the same kind have grown together in a certain symmetrical manner, such that one portion of the twin may be brought into the position of the other by reflection across a plane or by rotation about an axis. The plane of reflection is called the twin-plane, and is parallel to one of the faces, or to a possible face, of the crystal: the axis of rotation, called the twin-axis, is parallel to one of the edges or perpendicular to a face of the crystal.
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| Fig. 81.—Twinned Crystal of Gypsum. |
Fig. 82.—Simple Crystal of Gypsum. |
In the twinned crystal of gypsum represented in fig. 81 the two portions are symmetrical with respect to a plane parallel to the ortho-pinacoid (100), i.e. a vertical plane perpendicular to the face b. Or we may consider the simple crystal (fig. 82) to be cut in half by this plane and one portion to be rotated through 180° about the normal to the same plane. Such a crystal (fig. 81) is therefore described as being twinned on the plane (100).
An octahedron (fig. 83) twinned on an octahedral face (111) has the two portions symmetrical with respect to a plane parallel to this face (the large triangular face in the figure); and either portion may be brought into the position of the other by a rotation through 180° about the triad axis of symmetry which is perpendicular to this face. This kind of twinning is especially frequent in crystals of spinel, and is consequently often referred to as the “spinel twin-law.”
In these two examples the surface of the union, or composition-plane, of the two portions is a regular surface coinciding with the twin-plane; such twins are called “juxtaposition-twins.” In other juxtaposed twins the plane of composition is, however, not necessarily the twin-plane. Another type of twin is the “interpenetration twin,” an example of which is shown in fig. 84. Here one cube may be brought into the position of the other by a rotation of 180° about a triad axis, or by reflection across the octahedral plane which is perpendicular to this axis; the twin-plane is therefore (111).
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| Fig. 83.—Spinel-twin. | Fig. 84.—Interpenetrating Twinned Cubes. |
Since in many cases twinned crystals may be explained by the rotation of one portion through two right angles, R. J. Haüy introduced the term “hemitrope” (from the Gr. ἡμι-, half, and τρόπος, a turn); the word “macle” had been earlier used by Romé d’Isle. There are, however, some rare types of twins which cannot be explained by rotation about an axis, but only by reflection across a plane; these are known as “symmetric twins,” a good example of which is furnished by one of the twin-laws of chalcopyrite.
Twinned crystals may often be recognized by the presence of re-entrant angles between the faces of the two portions, as may be seen from the above figures. In some twinned crystals (e.g. quartz) there are, however, no re-entrant angles. On the other hand, two crystals accidentally grown together without any symmetrical relation between them will usually show some re-entrant angles, but this must not be taken to indicate the presence of twinning.
Twinning may be several times repeated on the same plane or on other similar planes of the crystal, giving rise to triplets,
