Tetragonal crystal system

The tetragonal crystal system has three mutually perpendicular crystallographic axes, with two equal lengths and a third of different length. Its symmetry includes a fourfold rotation axis.

Crystal system: A classification of crystals based on their symmetry and unit-cell geometry. Tetragonal is one of the seven crystal systems defined by these criteria.
Tetragonal point groups: The seven crystallographic point groups compatible with tetragonal symmetry. They specify the distinct symmetry operations possible within this crystal system.
Cubic crystal system: A crystal system with three equal, mutually perpendicular axes. Both systems have right angles, but cubic crystals have all three axes equal.
Zircon: A zirconium silicate mineral that commonly crystallizes in the tetragonal system. Its crystal structure is a prominent natural example of tetragonal symmetry.
Unit cell: The repeating three-dimensional building block that describes a crystal lattice. Its edge lengths and angles give the tetragonal system its defining geometry.
Tetragonal crystal class: A symmetry class whose crystals possess a principal fourfold axis. The class captures the defining rotational symmetry behind tetragonal geometry.
Orthorhombic crystal system: A crystal system with three unequal, mutually perpendicular axes. It shares tetragonal right angles but lacks a pair of equal axes and fourfold symmetry.
Rutile: A titanium dioxide mineral with a tetragonal crystal structure. Its elongated crystals display a familiar tetragonal form.
Crystallographic axis: A reference direction used to describe a crystal's geometry and symmetry. The system's three mutually perpendicular axes have two equal lengths.
Primitive tetragonal lattice: A tetragonal lattice with lattice points only at the unit-cell corners. It is one of the two Bravais lattice types allowed in the system.

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