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Outer automorphisms of free groups are largely studied via their action on Culler-Vogtmann Outer space. However, unlike in hyperbolic space or Teichmuller space (surface) settings, the dynamically minimal (fully irreducible) free group outer automorphisms act on Culler-Vogtmann Outer space with a collection of axes, whose closure is the Handel-Mosher ``axis bundle.'' Not much of the structure of this axis bundle has yet been understood. Together with Chi Cheuk Tsang, we prove that the axis bundle has a "cubist" structure and use this structure to find preferred axes for these outer automorphisms. We then use these axes to provide a solution to the fully irreducible conjugacy problem. This work can be seen as in analogy with that of Hamenstadt and Agol in the surface setting.