There are seven basic crystal shapes: cubic (isometric), tetragonal, orthorhombic, hexagonal, trigonal, triclinic and monoclinic. A crystal's shape is determined by one of seven crystal lattice systems, which are used to describe the crystal's geometric symmetry.
All crystals can be described by the Bravais Crystal Lattices, an assemblage of types of crystal lattices and the rules that define them. Isometric crystals are defined by one lattice point on each corner of a cube, and each lattice point divided congruently between eight adjacent cubes. Tetragonal crystals result from rectangular prisms with a square base, caused by stretching one cubic lattice along a vector. When stretched along two cubic vectors, an orthorhombic crystal results, wherein a rectangular prism has a rectangular base.
A hexagonal prism follows that of a right prism, and has a hexagonal base. A trigonal, or rhomohedral crystal has vectors of congruent length that are not all orthogonal. The trigonal crystal features a three-fold axis, unlike the hexagonal's six-fold axis. A crystal lattice with vectors of unequal length that are not mutually orthogonal is a triclinic crystal. A seventh crystal shape exists, the monoclinic shape. Monoclinic crystals form prisms and double pyramids; their lattices are formed by vectors of noncongruent length that form a rectangular prism.