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Cubic System
Cubic crystals come in several different shapes. They may be perfect cubes with six sides. They may also resemble two four-sided pyramids stuck together at the base; this structure is called an octahedron, or an eight-sided figure. Cubic system crystals may also have 12 faces. The best way to identify cubic crystals is by the shape and size of their faces; dodecahedrons and cubes will both have square faces of basically equal sizes. Octahedrons will have eight equally-sized faces shaped like equilateral triangles. Garnets, golden pyrite, diamonds and fluorite are all cubic crystals.
Tetragonal System
Tetragonal system crystals are similar to cubic crystals, except they are longer along one side than cubic crystal faces. For example, if a cubic crystal looks like a perfect six-sided cube, a tetragonal crystal will look like a six-sided cube with rectangular faces. Tetragonal octahedrons also look like two pyramids stuck together, but the pyramid faces are isosceles triangles with two longer sides and a shorter base rather than all three sides being equal, as in cubic octahedrons. Zircon is one example of a tetragonal crystal.
Orthorhombic System
Orthorhombic is one of the largest crystal systems. Orthorhombic crystals are usually long with rectangular facets that taper off to a pyramid shape near the top. If you look at these crystals from the non-tapered end, they should resemble flattened rectangles. The orthorhombic crystal system contains topaz, peridot, tanzanite and many types of quartz.