Author: Jan Scholten
Based on the crystal axes and the angles at which the axes intersect, crystals are divided into seven systems including, Cubic, Tetragonal, hexagonal, trigonal, Orthorhombic, Monoclinic, and Triclinic systems.
All three axes have the same length and intersect at right angel. Gem stones from cubic system form there basic shape, including cube, octahedron, dodecahedron.
The three axes intersect at right angles. Two of the axes have the same length and are located in the same plane. The main axis can be either longer or shorter. Gem stones from cubic system form there basic shape, including tetragonal prism, dipyramid, pyramid with prism.
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Three of the four axes have the same length and are located in one plane. These axes intersect each other at an angle of 120 degree. Typical crystal shapes are hexagonal prisms and pyramids, as well as twelve-sided pyramids and double pyramids.
Axes and the angles are similar to the hexagonal system. The difference is one of symmetry. In the case of hexagonal system, the cross section of the prism base is six sided; in trigonal system it is three-sided. Typical crystal forms of the trigonal system are three-sided prisms and pyramids, rhombohedra, and scalenohedra.
Three axes of different lengths are at right angles to each other. Typical crystal shapes are pinacoids, rhombic prisms, Pyramids, and Double pyramids.
The three axes are each of different length, two are at right angles to each other and the third one is inclined. Gemstones from monoclinic system form basic shapes of Basal pinacoids and prisms with inclined end faces.
All three axes are of different lengths and inclined to each other. Typical crystal forms are paired faces.
This is a lack of crystal structure.