a) Draw shapes in the plane which have the symmetry groups:
i. the dihedral group D8,
ii. the dihedral group D4,
iii. the cyclic group C5,
iv. the cyclic group C6.
b) Are there any shapes in the plane which have the symmetry group S4, the symmetric group on 4 letters? Either give an example, or explain why there are not any. A full mathematical proof is not needed.
I'm fine with part (a) which the dihedral group D8 is a square, D4 is a line, C5 and C6 are point groups. But i'm not sure about part (b), I know D8 is definitely in but not sure about others.
Any help would be appreciated. Thanks.