Crystals are built from of of seven, plus amorphous (without Internal structures), possible geometric forms that lock together into a number of potential crystal shapes, which have generic names based on their internal geometry. The outer form of the crystal will not necessarily reflect its inner structure but does affect how energy flows through it.
Cubic or Isometric
Not always cube shaped! You’ll also find octahedrons (eight faces) and dodecahedrons (10 faces). The simple cubic system has one lattice point on each corner of the cube with each lattice point shared equally between eight adjacent cubes.
Similar to cubic crystals, but longer along one axis than the other, forming double pyramids and prisms. Tetragonal crystal lattices result from stretching a cubic lattice along one lattice vectors, making the cube a rectangular prism with a square base.
Like tetragonal crystals except not square in cross section (when viewing the crystal on end), forming rhombic prisms or dipyramids (two pyramids stuck together). Orthorhombic lattices are made by stretching a cubic lattice along two lattice vectors by two factors, forming a rectangular prism with a rectangular base. All three bases intersect at 90° angles and the three lattice vectors are mutually orthogonal.
Six-sided prisms. When you look at the crystal on-end, the cross section is a hexagon. A hexagonal lattice has the same symmetry as a right prism with a hexagonal base. Graphite is an example of a hexagonal crystal.
Usually not symmetrical from one side to the other, which can lead to some fairly strange shapes. A triclinic crystal is described by vectors of unequal length. All three vectors are not mutually orthogonal.
Like skewed tetragonal crystals, often forming prisms and double pyramids. A monoclinic lattice is described by vectors of unequal length that form a rectangular prism with a parallelogram as base. Two pairs of vectors are perpendicular, while the third pair makes an angle other than 90°.
Possess a single 3-fold axis of rotation instead of the 6-fold axis of the hexagonal division. The rhombohedral (or trigonal) crystal is described by vectors of equal length, all three of which are not mutually orthogonal. You can think of the rhombohedral system as the cubic system stretched along a body diagonal.