This correlation in the case of can be described geometrically using the model of the real projective plane which is a "unit sphere with antipodes identified", or equivalently, the model of lines and planes through the origin of the vector space . Associate to any line through the origin the unique plane through the origin which is perpendicular (orthogonal) to the line. When, in the model, these lines are considered to be the points and the planes the lines of the projective plane , this association becomes a correlation (actually a polarity) of the projective plane. The sphere model is obtained by intersecting the lines and planes through the origin with a unit sphere centered at the origin. The lines meet the sphere in antipodal points which must then be identified to obtain a point of the projective plane, and the planes meet the sphere in great circles which are thus the lines of the projective plane.