1. Operations of the 1st kind. no change in handedness. rotation Cn
Operations of the 1st kind no change in handedness rotation Cn translation T

2. Operations of the 2nd kind. change in handedness - enantiomorphic
Operations of the 2nd kind change in handedness - enantiomorphic mirror m inversion i

3. Operations of the 2nd kind. change in handedness - enantiomorphic
Operations of the 2nd kind change in handedness - enantiomorphic mirror m

4. Operations of the 2nd kind. change in handedness - enantiomorphic
Operations of the 2nd kind change in handedness - enantiomorphic mirror m m m = 1 R L m

5. Operations of the 2nd kind. change in handedness - enantiomorphic
Operations of the 2nd kind change in handedness - enantiomorphic mirror m m m = 1 R L m

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

7. Operations of the 2nd kind. change in handedness - enantiomorphic
Operations of the 2nd kind change in handedness - enantiomorphic mirror m inversion i

8. Another operation of the 2nd kind. hint: combine operations of
Another operation of the 2nd kind hint: combine operations of 1st & 2nd kinds Ans:

9. Another operation of the 2nd kind Some examples of rotoinversions:

10. More combinations C2 T (2-D) :
Rule:

11. More combinations m T (2-D) :
Rule:

12. More combinations m T (2-D) :
Rule:

13. More combinations C2 T (2-D) :
Rule:

14. More combinations C3 T (2-D) :
Rule:

15. More combinations C3 T (2-D) :
Rule:

16. More combinations C3 T (2-D) :
Rule:

17. More combinations C3 T (2-D) :
Rule:
New symmetry element on bisector of T

18. More combinations C4 T (2-D) :
Rule:

19. More combinations C4 T (2-D) :
Rule:
New elements on bisectors - include
subgroups

20. More combinations C6 T (2-D) :
Rule:
New elements on bisectors - include
subgroups