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Again, there are some minerals which have the same chemical composition and yet crystallize in forms belonging to two different systems. Such minerals are said to be dimorphous. Other substances may form crystals of the same system and yet their angular elements may differ slightly. Alternatively, there are some chemical elements or compounds which will replace each other without altering the crystallographic characters of the compound in which the change takes place. Such substances are termed iso-morphous, and this property of isomorphism is possessed by some gem stones of importance, such as garnet.

The various types of crystals have been arranged in thirty-two possible groups, according to their symmetry, and these groups have been further classified into six systems, according to the relative length and inclination of the crystallographic axes. These six systems may be briefly described as follows:

1. Cubic System  (sometimes called Isometric, Monometric, Tes-seral, or Regular System).
Three equal and interchangeable axes at right angles to each other. Typical forms are the cube (fluor is a good example of a stone usually occurring in this form), the octahedron, e.g. diamond and spinel, and the dodecahedron, e.g. garnet. There are nine planes of symmetry in crystals of this system.
2.    Tetragonal System (sometimes called the Dimetric, Quadratic,
or Pyramidal System).
Three axes at right angles. The vertical axis is longer or shorter than the other two equal lateral axes. A typical form is the four sided prism, terminated by four triangular faces, e.g. zircon. There are five planes of symmetry.
3.    Hexagonal System.
Four axes. The vertical axis is longer or shorter than the other three, to which it is inclined at right angles. The other three lateral axes are equal, and intersect at an angle of 60 ° with each other. A typical form is a six-sided prism, terminated by a single face, e.g. emerald. Quartz, beryl, and tourmaline are among the minerals which belong to this system, in which there are seven planes of symmetry.
4.    Orthorhombic  System   (sometimes  known as  the  Rhombic,
Trimetric, and Prismatic System).
Three axes, which are all unequal but at right angles to each other. Crystals are usually prismatic in shape, e.g. topaz, peridot, and chrysoberyl. There are three planes of symmetry in this system.
5.    Monoclinic System (sometimes called the Oblique, Monosym-
metric, and Clino-rhombic System).
Three axes, two at right angles and the third inclined, all un equal in length. One plane of symmetry only.
6.    Triclinic System   (also known as the Anorthic, Doubly Ob
lique, and Asymetric System).
Three axes, all unequal, and all inclined to each other at different angles. There is no symmetrical plane.
Crystal forms may be divided into pyramid, prism, dome, and pinacoid types. For the sake of brevity, we will tabulate them thus:

(a)    Pyramid Forms. Each face composing this form cuts three crystallographic axes, or would cut them if both faces and axes were produced.
(b)    Prism Forms. Each face cuts the two lateral crystallographic faces and is parallel to the vertical axis. It is thus a vertical form.
(c)    Dome Forms. Each face cuts the vertical axis and one of the lateral axes, and is parallel to the other lateral axis.
(d)    Pinacoid Forms. Each face cuts one axis and is parallel to the other two.
It is somewhat difficult to visualize the axes and planes of symmetry of solid forms, and involved diagrams would probably not make this any clearer to the reader. Much more can be gained by inspecting natural crystals of a perfect form, or by making such forms from wood. The latter are easily obtained should the reader be interested in the study of crystallography, a science which not only has a great bearing on the proper understanding of gem stones but also on the structure and properties of all matter.