Fixed points of isometry groups in Euclidean space
（重定向自Centre of symmetry）
A fixed point of an isometry group is a point that is a fixed point for every isometry in the group. For any isometry group in Euclidean space the set of fixed points is either empty or an affine space.
For an object, any unique center and, more generally, any point with unique properties with respect to the object is a fixed point of its symmetry group.