Point group

In geometry, a point group is a group of geometric symmetries (isometries) that keep at least one point fixed. Point groups can exist in a Euclidean space with any dimension, and every point group in dimension d is a subgroup of the orthogonal group O(d). Point groups can be realized as sets of orthogonal matrices M that transform point x into point y: y = Mx where the origin is the fixed point. Point-group elements can either be rotations (determinant of M = 1) or else reflections, or improper rotations (determinant of M = −1).

Point group

In geometry, a point group is a group of geometric symmetries (isometries) that keep at least one point fixed. Point groups can exist in a Euclidean space with any dimension, and every point group in dimension d is a subgroup of the orthogonal group O(d). Point groups can be realized as sets of orthogonal matrices M that transform point x into point y: y = Mx where the origin is the fixed point. Point-group elements can either be rotations (determinant of M = 1) or else reflections, or improper rotations (determinant of M = −1).