Definition:Symmetry Group of Regular Pentagon

Group Example
Let $\PP = ABCDE$ be a regular pentagon.


 * Symmetry-Group-of-Regular-Pentagon.png

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 $t_A, t_B, t_C, t_D, t_E$ about 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 known as
The symmetry group of the regular pentagon is also known as:
 * the dihedral group of order $10$ and denoted $D_5$

Some sources denote $D_5$ as ${D_5}^*$.

Also see

 * Symmetry Group of Regular Pentagon is Group


 * Definition:Dihedral Group