handouts/Advanced/Knots/parts/table.tex

\section{Table of Prime Knots}
A knot's \textit{crossing number} is the minimal number of crossings its projection must contain. In general, it is very difficult to determine a knot's crossing number.

\vspace{1mm}

This table contains the 15 smallest prime knots, ordered by crossing number. \par
Mirror images are not included, even if the mirror image produces a nonisomorphic knot.

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% Images are from the appendix of the Knot book.
{
	\def\w{24mm}
	\foreach \l/\c/\r in {%
		{3_1}/{4_1}/{5_1},%
		{5_2}/{6_1}/{6_2},%
		{6_3}/{7_1}/{7_2},%
		{7_3}/{7_4}/{7_5},%
		{7_6}/{7_7}/{8_1}%
	}{
		\hfill
		\begin{minipage}{\w}
		\begin{center}
			\includegraphics[width=\linewidth]{knot table/\l.png} \par
			\vspace{2mm}
			{\huge $\l$}
		\end{center}
		\end{minipage}
		\hfill
		\begin{minipage}{\w}
		\begin{center}
			\includegraphics[width=\linewidth]{knot table/\c.png} \par
			\vspace{2mm}
			{\huge $\c$}
		\end{center}
		\end{minipage}
		\hfill
		\begin{minipage}{\w}
		\begin{center}
			\includegraphics[width=\linewidth]{knot table/\r.png} \par
			\vspace{2mm}
			{\huge $\r$}
		\end{center}
		\end{minipage}
		\hfill~\par
		\vspace{4mm}
	}
}

\vfill
\pagebreak