There are crystal systems and lattice types. There are 7 crystal systems. These are triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic.
Lattices can either be primitive, with only one lattice point per unit cell, or non-primitive, with more than one lattice point per unit cell.
Crystals are also categorized by their physical and chemical properties. In this classification there are four types of crystals.
Covalent crystals are a crystal that has real chemical covalent between all of the atoms in the crystal. A single crystal of a covalent crystal is one big molecule. Covalent crystals have extremely high melting points. An example of a covalent crystal is a diamond or zinc sulfide.
Metallic crystals are individual metal atoms sitting on lattice sites while the outer electrons from these atoms are able to flow freely around the lattice. Metallic crystals normally have high melting points and densities.
The ionic crystal is a crystal where the individual atoms don’t have covalent bonds between them, but are held together by electrostatic forces. An example of this type of crystal is sodium chloride. Ionic crystals are hard and have relatively high melting points.
Molecular crystals is a crystal where there are recognizable molecules in the structure and the crystal is held together by non-covalent interactions like van der Waals forces or hydrogen bonding. An example of this type of crystal would be sugar. Molecular crystals tend to be soft and have lower melting points.