Rosettes
In mathematics the word "rosette" indicates a plane figure whose symmetry group (that is the set of all those transformations of the plane that leave distances unchanged and map the figure onto itself) contains only a finite number of transformations.
It can be proven that the only two possibilities for a rosette's symmetry group are cyclic groups (that are denoted with the symbol Cn and that contain n rotations) or dihedral (that are denoted with the symbol Dn and that contain n rotations and n reflections).
For any given integer number n, there is a corresponding cyclic group Cn and a corresponding dihedral group Dn.
| cyclic groups | dihedral group | ||
|---|---|---|---|
C1
|
C2
|
D1
|
D2
|
C3 |
C4 |
D3 |
D4
 |
C5
|
C6
 |
D5 |
D6 |
C7
|
C8
|
D7
|
D8
|
| ... |
...
|
... | ...
|
