Definition:Dihedral Group D5
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Example of Dihedral Group
Let $\PP = ABCDE$ be a regular pentagon.
The various symmetry mappings of $\PP$ are:
- the identity mapping $e$
- the rotations $r, r^2, r^3, r^4$ of $72^\circ, 144^\circ, 216^\circ, 288^\circ$ around the center of $\PP$ anticlockwise respectively
- the reflections $t_A, t_B, t_C, t_D, t_E$ in the lines through the center of $\PP$ and the vertices $A$ to $E$ respectively.
This group is known as the symmetry group of the regular pentagon.
- Results about the dihedral group $D_5$ can be found here.