An Introduction to Axes
A cube has three axes, all perpendicular to each other and all the same length. A rectangle, on the other hand, is defined by three axes, all perpendicular, but only two are the same length. If this is a little difficult to visualize, the best descriptions and drawings of three-dimensional shapes are found in geometry books.
Isometric
Isometric crystals are cube-shaped and are the most symmetrical of the six crystal types, making them easy to identify. However, a cube-shaped crystal may be modified and still be considered cube-shaped. For example, a cube whose corners are all neatly shaved off is still a cube.
Hexagonal
Hexagonal crystals are longer than they are wide and have six sides all the same length. Sapphire is a hexagonal crystal. Hexagonal crystals are also easy to recognize and among the most prized for pendants and decorating chandeliers.
Tetragonal
Tetragonal crystals are shaped like a three-dimensional rectangle. They have three axes, all perpendicular, but only two are of equal length. Apophyllite is an example of a tetragonal crystal.
Ortorhombic
Orthorhombic crystals look like a rectangle at first glance, but are different. They have three axes, all perpendicular, but all different lengths. Golden Topaz is an example of an orthorhombic crystal. Although its internal structure is orthorhombic, most jewelry made of Golden Topaz would be difficult to identify as such once it's cut into the familiar shapes of most rings and pendants.
Monoclinic and Triclinic Crystals
Monoclinic and triclinic crystals are the most difficult to describe by shape and axes, but examples are Gypsum and Orthoclase respectively. While many crystalline minerals are valued for their beauty and usefulness in jewelry-making, gypsum (hydrated calcium sulfate) is used mostly for making plaster and drywall.