| 11. | A distance-preserving diffeomorphism between Riemannian manifolds is called an isometry.
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| 12. | A second straightforward construction of the icosahedron uses isometries on the icosahedron.
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| 13. | Note that a quasi-isometry is not required to be continuous.
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| 14. | See also fixed points of isometry groups in Euclidean space.
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| 15. | The 2-4 tree isometry was described in 1978 by Sedgewick.
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| 16. | Apply first an isometry sending these directions to the coordinate axes of.
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| 17. | This shift operator is an isometry, therefore bounded below by 1.
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| 18. | Like any other bijection, a global isometry has a function inverse.
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| 19. | Every isometry group of a metric space is a subgroup of isometries.
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| 20. | Every isometry group of a metric space is a subgroup of isometries.
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