halfturn

A halfturn, also called a 180-degree rotation, is a geometric transformation that rotates points around a fixed center by half a full turn. In the plane, a halfturn about a center C maps every point P to a point P' such that C is the midpoint of PP', equivalently a central symmetry about C. It is an isometry of order two: applying it twice yields the original configuration.

In three dimensions, a halfturn usually refers to a 180-degree rotation about a fixed axis (a line through space). Such halfturns are also of order two and are central to many symmetry considerations, including crystallography, where a twofold rotation axis (C2) is common.

In group theory and geometry, halfturns are elements of order two within rotation groups and dihedral groups; they are the rotations by pi radians about some axis or point.

In practical usage, the term appears in sports and dance as a 180-degree spin. In Rubik’s Cube terminology, a half-turn denotes a 180-degree twist of a face; in the half-turn metric, such turns may be counted as a single move, just as 90-degree turns are in some other metrics.

Etymology: the term derives from turning halfway around.