In geometry, a polar point group is a point group in which there is more than one point that every symmetry operation leaves unmoved. The unmoved points will constitute a line, a plane, or all of space.
A straight line joining two unmoved points defines a unique axis of rotation, called a polar direction, unless the symmetry operations do not allow any rotation at all, such as mirror symmetry, in which case the polar direction must be parallel to any mirror planes.[clarification needed]
A point group with more than one axis of rotation or with a mirror plane perpendicular to an axis of rotation cannot be polar.
|Crystal system||Polar point groups|
When materials having a polar point group crystal structure are heated or cooled, they may temporarily generate a voltage called pyroelectricity.
Molecular crystals that occupy[clarification needed] polar space groups may exhibit triboluminescence. A common example of this is sucrose, demonstrated by smashing a wintergreen lifesaver in a darkened room.