7. Triclinic. There is no axis of symmetry of any kind, and there are no prominent directions at right angles. One of the two classes has a center of symmetry only, and the other no symmetry at all. Characterized by three noninterchangeable crystallographic axes, none at right angles.
A fact which should be strongly emphasized is that crystals only, of all the objects of nature, can be definitely referred to the above seven systems comprising the 32 classes of symmetry, and 232 crystal forms. Since there are about 1,000 mineral species and only 232 fundamental forms, it necessarily follows that two or more species may crystallize in the same form within a class, so that it is not always possible to tell the species of mineral merely by its crystal form. It is, however, a remarkable fact that, where two or more substances crystallize in the same class (i.e., show the same grade of symmetry) each substance almost invariably exhibits “crystal habit” which is a pronounced tendency to crystallize in certain relatively few forms or combinations of forms out of the many possibilities. It is clear, then, that grade of symmetry combined with “habit” are of great practical value in determining crystallized minerals, because, on the basis of symmetry, a crystal is referred to a certain definite symmetry class in which only a limited number of substances crystallize, and then, by its characteristic “habit,” the particular substance can be told.
Fig. 72.—Figures illustrating three crystal forms with exactly the same symmetry elements; a and b are separate forms, and c is a combination of the two. The mineral “garnet” nearly always crystallizes in one of these forms.
From the above discussion it should not be presumed that crystals always develop with perfect geometric symmetry. As a matter of fact such is seldom the case because, due to variations of conditions or interference of surrounding crystals in liquids (ordinary or molten), a crystal usually grows more rapidly (by building out faces) in certain directions than in others. Under such conditions actual crystals are said to become distorted because they are not geometrically perfect.
Whether geometrically perfect or not, all crystals respond to the law of constancy of interfacial angles which means that on all crystals of the same substances the angles between similar (corresponding) faces are always equal. This is one of the most fundamental and remarkable laws of minerals. That it must be true follows from the fact that the crystal faces merely outwardly express in definite form the definite internal structure or arrangement of particles which have built up the crystal. In other words, the real structural symmetry of a crystal never varies no matter how much its geometric symmetry may vary. The practical application of the law of constancy of interfacial angles lies in the fact that in many cases a mineral may actually be identified merely by measuring the interfacial angles of its crystal form.
The relative lengths of the crystallographic axes is a very important feature of all crystals except those of the isometric system in which the axes are always of equal length so that the ratio is 1:1:1. In all the other systems, however, at least one axis differs in length from the others and, since the amount of difference is absolutely characteristic of each substance, the axial ratio of a crystal, when carefully determined by measurement of the angles between the different faces, affords a never-failing method of determining the mineral for all systems except the isometric. By way of illustration, the tetragonal crystal of the mineral zircon, with only one axis different in length, shows the very definite axial ratio 1:1:0.64, while the orthorhombic crystal of sulphur, with all three axes of different lengths, has an axial ratio 0.813:1:1.903. These ratios of course always hold true no matter what the size or particular outward form of the crystal.
As might be expected from the above discussion of the remarkable structure of crystals, experience has proved that the relative lengths of all intercepts (or distances from the center) of all faces upon any crystal can be expressed by whole numbers, definite fractions, or infinity. It necessarily follows that the ratios between the intercepts of the faces of any face on a crystal to those of any other face on the same crystal may always be expressed by rational numbers, and this is known as the law of definite mathematical ratio. It is a remarkable fact that very small whole numbers or fractions, or infinity or zero, will always express the intercepts of any crystal face.
Thus far our discussion has centered about crystals as individuals, but, in most cases by far, they form groups or aggregates. Most commonly crystal grouping is very irregular, but by no means rare is parallel grouping where whole crystals, or more usually parts of crystals, have all corresponding parts exactly parallel. But most remarkable of all are the twin crystals in which two or more crystals intergrown or in contact have all corresponding parts in exactly reverse order. The conditioning circumstances under which twin crystals develop are unknown.