A crystal is a body bounded by surfaces, most often planar surfaces, that are arranged to reflect the internal arrangements of atoms.
The type of crystal formed by a mineral depends on the environment in which the mineral forms and the specific atoms that make up the mineral.
The structure of minerals have been cataloged, and geologists use that information to help identify minerals.
To describe crystals and distinguish between certain minerals, we often look at crystal symmetry.
If we can "slice" a structure along a plane and produce two pieces that are mirror images of one another, we call that plane a plane of symmetry.
If we can rotate a structure around an axis and reproduce the structure, we call the axis, an axis of symmetry (the angle has to be between 0° and 360°). The number of angles that reproduce the unrotated structure determines the "fold" of the rotation axis (e.g. two-fold, four-fold).