  We prove that a pair of heterodimensional cycles can be born at the
bifurcations of a pair of Shilnikov loops (homoclinic loops to a saddle-focus
equilibrium) having a one-dimensional unstable manifold in a volume-hyperbolic
flow with a $\mathbb{Z}_2$ symmetry. We also show that these heterodimensional
cycles can belong to a chain-transitive attractor of the system along with
persistent homoclinic tangency.
