Fixed points of isometry groups in Euclidean space

（重定向自Center 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.

单词	Center of symmetry
释义	Center of symmetry 原声例句 TED-Ed（视频版） But some crystalline materials don't possess a center of symmetry making them candidates for piezoelectricity. 但是一些晶体材料不具有对称中心，这使它们成为压电性的候选者。 TED-Ed（视频版） But what they all have in common is unit cells which lack a center of symmetry. 但它们的共同点是缺乏对称中心的晶胞。英语百科 Fixed points of isometry groups in Euclidean space （重定向自Center 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.
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