When grouped by shape or lattice, the seven types of crystals are cubic or isometric, orthorhombic, tetragonal, hexagonal, trigonal, triclinic and monoclinic. Crystals are also grouped by their chemical and physical properties.
The shapes of crystals are distinct but difficult to imagine until seen. Also, names can be misleading. For example, a cubic crystal is not always cube shaped. Within the isometric classification alone, there may be cube shapes, octahedrons (eight faces) and dodecahedrons (10 faces). Most classes and shapes are symmetrical, but the triclinic class is usually asymmetrical, making for some strange crystal shapes.
Chemical properties that are used to group crystals include covalent, metallic, ionic and molecular. There are distinct differences in each of these. For instance, a covalent crystal has bonds between all the atoms in the crystal, like one big molecule, but a molecular crystal is made up of many molecules in one big lump. Ionic crystals have bonds between all the atoms similar to a covalent crystal, but the ionic crystals have bonds of a more electrostatic nature. This makes their melting points much higher than the covalent crystals. Metallic crystals have metal atoms in specific lattice works, but the outer metal atoms are free to move about.