Create Plane Figures w/ Non-Isomorphic 12 Element Symmetry Groups

  • Thread starter Thread starter MikeDietrich
  • Start date Start date
  • Tags Tags
    Plane
Join the discussion
Registration is free. Ask a follow-up in this thread, or start your own.
Sign up Log in
1 reply · 2K views
MikeDietrich
Messages
31
Reaction score
0

Homework Statement


Draw two plane figures, each having a 12 element group of symmetries, such that the two groups are NOT isomorphic. Demonstrate that they are not isomorphic.

Homework Equations


I know that every finite group of isometries of the plane is isomorphic to either Z_n or to the dihedral group D_n.

The Attempt at a Solution


I drew a regular hexagon (D_6) but now I am stuck as to what to draw for a figure to represent Z_12. Would a 12 bladed windmill (pinwheel) type shape with pronged ends work?
 
Last edited:

Discussion

Physics news on Phys.org
Yes, this will work, since it is not preserved by a reflection.