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Plane Isometries 
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#1
Dec1210, 06:41 PM

P: 31

1. The problem statement, all variables and given/known data
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. 2. Relevant 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. 3. 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? 


#2
Dec1210, 10:09 PM

P: 352

Yes, this will work, since it is not preserved by a reflection.



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