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