Created the Abstract Algebra theorems and definitions cheat sheet

2024-01-09 11:30:56 -07:00
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+\section{Identification of Plane Periodic Patterns}
+
+\begin{remark}
+	A \textit{lattice of points} of a pattern is a set of images of any particular point acted on by the translation group of the pattern. A \textit{lattice unit} of a pattern whose translation subgroup is generated by $u$ and $v$ is a parallelogram formed by a point of the pattern and its image under $u,v$, and $u + v$. A \textit{generating region} (or \textit{fundamental region}) of a periodic pattern is the smallest portion of the lattice unit whose images under the full symmetry of the group of the pattern cover the plane.
+\end{remark}