We calculate the low-lying spectrum of the $\mathrm{<mrow\; data-mjx-texclass="ORD">16</mrow>}$O nucleus using an α-cluster model which includes the important tetrahedral and square configurations. Our approach is motivated by the dynamics of α-particle scattering in the Skyrme model. We are able to replicate the large energy splitting that is observed between states of identical spin but opposite parities. We also provide a novel interpretation of the first excited state of $\mathrm{<mrow\; data-mjx-texclass="ORD">16</mrow>}$O and make predictions for the energies of 6$\mathrm{<mrow\; data-mjx-texclass="ORD">-</mrow>}$ states that have yet to be observed experimentally.