Crystal lattice

Main article: Crystal lattice.

Crystal structure - the infinite three-dimensional periodic lattice that is composed from substances` particles (such as molecules, atoms, etc.)
Crystal lattice - the elementary three-dimensional cell of crystal structure which completely determines its properties. In the general case it is a slanted parallelepiped (sometimes more than one) from the particles which are located in its nodes, edges, etc.

Lattice classification

There are many classifications of crystal lattices - by particle type (chemical), by lattice common shape (singony), by type of symmetry of the lattice (crystal system), by type of spatial translations (Bravais lattice), etc.
There you can find only the basic classifications.

Chemical

In the chemical classification lattices are combined into four kinds by the type of the constituent particles.

Lattice type	Lattice nodes	Examples
Atomic	Atoms of nonmetal elements	Diamond, graphite, selenium
Molecular	Molecules of non-ionic compounds	Water, carbon dioxide, sucrose
Ionic	Cations and anions of salts, acids, alkalines	Table salt, citric acid, copper(II) sulfate
Metallic	Atom-ions of metal elements and their shared electrons	Iron, copper, lead, nickel

Crystal system, singony, system of lattice

Main atricle: Crystal system (wikipedia).
Main atricle: Crystal system.

The crystal system classification focuses on sets of axes which the lattice can be rotated around less than 360 ° and combined with the non-rotaned one.
The syngony classification focuses on lattices with similar angles and specific distances between nodes.
The system of lattice classification focuses on lattices` symmetry types.

Despite the fact that the defined parameters of all three classification systems are completely different, geometric properties of crystal shapes allow to almost clearly establish the correspondence between them. They are often used as synonyms for each other as they describe finite lattices approximately the same way.

Notice that in Crystal growing project pages all of these terms mean crystal system.

Symmetry category	Singony	Crystal system	System of lattice	Count of matches by rotating around the symmetry axis	Count of symmetry axises
Low symmetric	Triclinic			None	None
	Monoclinic			Two	One
	Orthorhombic			Two	Three
Medium symmetric	Tetragonal			Four	One
	Hexagonal	Trigonal	Rhombohedral	Three	One
		Trigonal	Hexagonal	Six	One
		Hexagonal		Six	One
High symmetric	Cubic			Four	Three

Crystal shape

Main article: Form.

There you can find all existing 47 simple forms of crystals depending on the crystal system.
It is worth noting that crystals rarely grow in their simplest form, there are often various counterparts, truncation, beveled edges and many other distortions can be found.