text: Usually when describing a space geometrically, a coordinate system is used which consists of a choice of origin and a basis of  linearly independent, non-coplanar basis vectors , where  is the dimension of the space being described. With reference to this coordinate system, each point in the space can be specified by  coordinates (a coordinate -tuple). The origin has coordinates  and an arbitrary point has coordinates . The position vector  is then, 
  In -dimensions, the lengths of the basis vectors are denoted  and the angles between them . However, most cases in crystallography involve two- or three-dimensional space in which the basis vectors  are commonly displayed as  with their lengths and angles denoted by  and  respectively.