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Operations of the 1st kind no change in handedness rotation C n translation T

Explore operations in spatial transformations involving changes in handedness, enantiomorphic mirrors, inversions, and more. Learn how combining operations of the first and second kinds can yield important results, particularly in translations. Discover new symmetry elements and subgroups.

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Operations of the 1st kind no change in handedness rotation C n translation T

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  1. Operations of the 1st kindno change in handednessrotation Cn translationT

  2. Operations of the 2nd kindchange in handedness - enantiomorphicmirror m inversioni

  3. Operations of the 2nd kindchange in handedness - enantiomorphicmirror m

  4. Operations of the 2nd kindchange in handedness - enantiomorphicmirror m m m = 1 R m L

  5. Operations of the 2nd kindchange in handedness - enantiomorphicmirror m m m = 1 R R m m L L

  6. Operations of the 2nd kindchange in handedness - enantiomorphicmirror m m m = 1 2 successive 2nd kind operations give 1st kind operation - important when translations involved

  7. Operations of the 2nd kindchange in handedness - enantiomorphicmirror m inversioni

  8. Another operation of the 2nd kindhint: combine operations of 1st & 2nd kindsAns:

  9. Another operation of the 2nd kindSome examples of rotoinversions:

  10. More combinationsC2 T (2-D) : Rule:

  11. More combinationsm T (2-D) : Rule:

  12. More combinationsm T (2-D) : Rule:

  13. More combinationsC2 T (2-D) : Rule:

  14. More combinationsC3 T (2-D) : Rule:

  15. More combinationsC3 T (2-D) : Rule:

  16. More combinationsC3 T (2-D) : Rule:

  17. More combinationsC3 T (2-D) : Rule: New symmetry element on bisector of T

  18. More combinationsC4 T (2-D) : Rule:

  19. More combinationsC4 T (2-D) : Rule: New elements on bisectors - include subgroups

  20. More combinationsC6 T (2-D) : Rule: New elements on bisectors - include subgroups

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