Fractional coordinates
In crystallography, a fractional coordinate system (crystal coordinate system) is a coordinate system in which basis vectors used to describe the space are the lattice vectors of a crystal (periodic) pattern. The selection of an origin and a basis define a unit cell, a parallelotope (i.e., generalization of a parallelogram (2D) or parallelepiped (3D) in higher dimensions) defined by the lattice basis vectors a 1 , a 2 , … , a d {\displaystyle \mathbf {a} _{1},\mathbf {a} _{2},\dots ,\mathbf {a} _{d}} where d {\displaystyle d} is the dimension of the space.