Definition:Symmetry Group of Parallelogram
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Group Example
Let $\PP = ABCD$ be a (non-rectangular) parallelogram.
The various symmetry mappings of $\PP$ are:
- The identity mapping $e$
- The rotation $r$ (in either direction) of $180^\circ$.
The symmetries of $\PP$ form the dihedral group $D_1$.
Cayley Table
The Cayley table of the symmetry group of the (non-rectangular) parallelogram can be written:
- $\begin{array}{c|cccc}
& e & r \\
\hline e & e & r \\ r & r & e \\ \end{array}$
Sources
- 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $1$: Definitions and Examples: Exercise $4 \ \text{(b)}$