improper_ring.tex
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	\documentclass[12pt]{article}

	\begin{document}

	\begin{eqnarray*}
	E & = &\frac{1}{6} K \left(\Delta_{ijl} + \Delta_{ijk} + \Delta_{kjl} \right)^6 \\
	\Delta_{ijl} & = & \cos{\theta_{ijl} - \cos{\theta_0}} \\
	\Delta_{ijk} & = & \cos{\theta_{ijk} - \cos{\theta_0}} \\
	\Delta_{kjl} & = & \cos{\theta_{kjl} - \cos{\theta_0}}
	\end{eqnarray*}

	\end{document}