Category:Dihedral Group D4

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This category contains examples of Dihedral Group D4.

The dihedral group $D_4$ is the symmetry group of the square:

Let $\mathcal S = ABCD$ be a square.

SymmetryGroupSquare.png

The various symmetry mappings of $\mathcal S$ are:

The identity mapping $e$
The rotations $r, r^2, r^3$ of $90^\circ, 180^\circ, 270^\circ$ counterclockwise respectively about the center of $\mathcal S$.
The reflections $t_x$ and $t_y$ are reflections about the $x$ and $y$ axis respectively.
The reflection $t_{AC}$ is a reflection about the diagonal through vertices $A$ and $C$.
The reflection $t_{BD}$ is a reflection about the diagonal through vertices $B$ and $D$.

This group is known as the symmetry group of the square.

Subcategories

This category has only the following subcategory.

Pages in category "Dihedral Group D4"

The following 45 pages are in this category, out of 45 total.

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