A few good necessary and sufficient conditions are given by using length relation for symmetrical transformation on Euclidean space.
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袁晖坪.长度关系与对称变换[J].重庆工商大学学报(自然科学版),1997,(3): Yuan Huiping. Length Relation and Symmetrical Transformation[J]. Journal of Chongqing Technology and Business University(Natural Science Edition),1997,(3):