  In this paper we proceed into the next step of formalization of a consistent
dual theory for mass dimension one spinors. This task is developed approaching
the two different and complementary aspects of such duals, clarifying its
algebraic structure and the so called $\tau-$deformation. The former regards
the mathematical equivalence of the recent proposed Lorentz preserving dual
with the duals of algebraic spinors, from Clifford algebras, showing the
consistency and generality of the new dual. Moreover, by revealing its
automorphism structure, the hole of the $\tau-$deformation and contrasting the
action group orbits with other Lorentz breaking scenarios, we argue that the
new mass dimension one dual theory is placed over solid and consistent basis.
