Crystal system
A set of point groups classifying crystal symmetries.
In crystallography, a crystal system is a set of point groups, which are groups of geometric symmetries with at least one fixed point. Crystal systems are one of three ways to classify crystals, alongside lattice systems and crystal families, though the term is sometimes confused with those other classifications. Space groups are classified into crystal systems according to their point groups.
- field
- Crystallography
- known_for
- Classification of crystals into 7 crystal systems in 3 dimensions, 33 in 4 dimensions
Lore & Background
In two-dimensional space, crystal families, crystal systems, and lattice systems are identical, comprising four families: oblique, rectangular, square, and hexagonal. In three-dimensional space, there are 7 crystal systems: triclinic, monoclinic, orthorhombic, tetragonal, cubic, trigonal, and hexagonal. Five of these—triclinic, monoclinic, orthorhombic, tetragonal, and cubic—are essentially the same as five lattice systems.
Reader's Guide
The 7 crystal systems consist of 32 crystal classes, corresponding to the 32 crystallographic point groups. Notably, 5 point groups have 7 corresponding space groups assigned to the rhombohedral lattice system and 18 to the hexagonal lattice system; these point groups are assigned to the trigonal crystal system. The hexagonal and trigonal crystal systems differ from the hexagonal and rhombohedral lattice systems, and are combined into the hexagonal crystal family. In four-dimensional space, there are 33 crystal systems. The term 'crystal system' is sometimes used interchangeably with 'lattice system' or 'crystal family,' leading to confusion, particularly with the trigonal crystal system often mistaken for the rhombohedral lattice system.
Did You Know?
- In three-dimensional space, there are 7 crystal systems and 7 lattice systems.
- Five of the 3D crystal systems are essentially the same as five lattice systems: triclinic, monoclinic, orthorhombic, tetragonal, and cubic.
- The trigonal crystal system is often confused with the rhombohedral lattice system; there is no 'trigonal' lattice system.
- In four-dimensional space, there are 33 crystal systems.
Frequently Asked Questions
What exactly is a Crystal system?
In crystallography, a Crystal system is a collection of point groups—sets of geometric symmetry operations that all share at least one fixed point. It serves as one of three primary schemes for organizing and classifying crystals.
How many Crystal systems exist?
In three-dimensional space there are exactly seven Crystal systems. In four-dimensional space the count expands to thirty-three.
What's the difference between a Crystal system and a lattice system?
A Crystal system is defined by its point groups (symmetry operations around a fixed point), while lattice systems and crystal families are two separate classification frameworks. The three are related but distinct, and their names are frequently confused.
How do Crystal systems relate to space groups?
Space groups are assigned to a Crystal system based on the point group they contain, making the Crystal system a key organizing category within the broader space-group hierarchy.
Why does the Crystal system classification matter?
It gives crystallographers a symmetry-based way to group crystals that is independent of their lattice geometry, providing a complementary lens alongside lattice systems and crystal families.
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