# 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.

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.

### C

### D

- Dihedral Group D4 is not Internal Group Product
- Dihedral Group D4/Cayley Table
- Dihedral Group D4/Cayley Table/Coset Decomposition of (e, a, a^2, a^3)
- Dihedral Group D4/Cayley Table/Coset Decomposition of (e, a^2)
- Dihedral Group D4/Center
- Dihedral Group D4/Group Presentation
- Dihedral Group D4/Matrix Representation
- Dihedral Group D4/Matrix Representation/Formulation 1
- Dihedral Group D4/Matrix Representation/Formulation 1/Cayley Table
- Dihedral Group D4/Matrix Representation/Formulation 2
- Dihedral Group D4/Matrix Representation/Formulation 2/Cayley Table
- Dihedral Group D4/Matrix Representation/Formulation 2/Examples of Cosets
- Dihedral Group D4/Matrix Representation/Formulation 2/Examples of Cosets/Subgroup Generated by A
- Dihedral Group D4/Matrix Representation/Formulation 2/Examples of Cosets/Subgroup Generated by A/Left Cosets
- Dihedral Group D4/Matrix Representation/Formulation 2/Examples of Cosets/Subgroup Generated by A/Right Cosets
- Dihedral Group D4/Matrix Representation/Formulation 2/Examples of Cosets/Subgroup Generated by B, F
- Dihedral Group D4/Matrix Representation/Formulation 2/Examples of Cosets/Subgroup Generated by B, F/Left Cosets
- Dihedral Group D4/Matrix Representation/Formulation 2/Examples of Cosets/Subgroup Generated by B, F/Right Cosets
- Dihedral Group D4/Matrix Representation/Formulation 2/Examples of Cosets/Subgroup Generated by D
- Dihedral Group D4/Matrix Representation/Formulation 2/Examples of Cosets/Subgroup Generated by D/Left Cosets
- Dihedral Group D4/Matrix Representation/Formulation 2/Examples of Cosets/Subgroup Generated by D/Right Cosets
- Dihedral Group D4/Matrix Representation/Formulation 2/Examples of Generated Subgroups
- Dihedral Group D4/Matrix Representation/Formulation 2/Examples of Generated Subgroups/A
- Dihedral Group D4/Matrix Representation/Formulation 2/Examples of Generated Subgroups/A, C
- Dihedral Group D4/Matrix Representation/Formulation 2/Examples of Generated Subgroups/A, D
- Dihedral Group D4/Matrix Representation/Formulation 2/Examples of Generated Subgroups/B, F
- Dihedral Group D4/Matrix Representation/Formulation 2/Examples of Generated Subgroups/D
- Dihedral Group D4/Normal Subgroups
- Dihedral Group D4/Normal Subgroups/Subgroup Generated by a
- Dihedral Group D4/Normal Subgroups/Subgroup Generated by a^2
- Dihedral Group D4/Normal Subgroups/Subgroup Generated by a^2, b
- Dihedral Group D4/Normal Subgroups/Subgroup Generated by a^2/Quotient Group
- Dihedral Group D4/Normal Subgroups/Subgroup Generated by a^2/Quotient Group/Subgroups
- Dihedral Group D4/Subgroups
- Dihedral Group D4/Subgroups/Cosets
- Dihedral Group D4/Subgroups/Cosets/Subgroup Generated by b
- Dihedral Group D4/Subgroups/Cosets/Subgroup Generated by b/Left Cosets
- Dihedral Group D4/Subgroups/Cosets/Subgroup Generated by b/Right Cosets