The stereographic projection is often used to represent the angular relations between directions and planes in a crystal. This projection system can be visualized by imagining a tiny (infinitesimal) crystal at the center of a sphere. All of the planes and directions of interest are extended until they intersect the surface of the sphere. Directions intersect the sphere as points and planes intersect it as great circles, as shown in Figure B.1 These points and great circles are then projected onto a flat surface. See Figure B.2 The problem of plotting these on a flat surface is exactly the same as the mapmaker's problem of plotting the spherical surface of the earth. For crystals, it is necessary to plot only half of the spherical surface, because the opposite hemisphere is identical. Barrett and Cullity describe the details of stereographic projection.