Isometry

In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective.^[a] The word isometry is derived from the Ancient Greek: ἴσος isos meaning "equal", and μέτρον metron meaning "measure". If the transformation is from a metric space to itself, it is a kind of geometric transformation known as a motion.

^ Coxeter 1969, p. 46
3.51 Any direct isometry is either a translation or a rotation. Any opposite isometry is either a reflection or a glide reflection.
^ Coxeter 1969, p. 29

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[1] Coxeter 1969, p. 46
3.51 Any direct isometry is either a translation or a rotation. Any opposite isometry is either a reflection or a glide reflection.

[2] Coxeter 1969, p. 29

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