The resonant substructure of the decay $D^{0} \rightarrow \pi^{+} \pi^{-} \pi^{+} \pi^{-}$ is studied by performing a full five-dimensional amplitude analysis. Preliminary results based on data collected by the CLEO-c detector are presented. This is the largest dataset of $D^{0} \rightarrow \pi^{+} \pi^{-} \pi^{+} \pi^{-}$ decays analysed in this way to-date. The two most significant contributions are $D^{0} \to a_{1}(1260)^{+} \, \pi^{-}$ and $D^{0} \to \rho(770)^{0} \, \rho(770)^{0}$. The line shape, mass and width of the $a_{1}(1260)$ resonance are determined, and model-independent studies of the line shapes of several resonant contributions are preformed.