Definition:Dihedral Group D5

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Example of Dihedral Group

The dihedral group $D_5$ is the symmetry group of the regular pentagon:

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.

Also see

  • Results about the dihedral group $D_5$ can be found here.