In geometry, a polar point group is a point group in which there is more than one point that every symmetry operation leaves unmoved.[1] The unmoved points will constitute a line, a plane, or all of space.
While the simplest point group, C1, leaves all points invariant, most polar point groups will move some, but not all points. To describe the points which are unmoved by the symmetry operations of the point group, we draw a straight line joining two unmoved points. This line is called a polar direction. The electric polarization must be parallel to a polar direction. In polar point groups of high symmetry, the polar direction can be a unique axis of rotation, but if the symmetry operations do not allow any rotation at all, such as mirror symmetry, there can be an infinite number of such axes: in that case the only restriction on the polar direction is that it must be parallel to any mirror planes.
A point group with more than one axis of rotation or with a mirror plane perpendicular to an axis of rotation cannot be polar.