  We construct two more supersymmetric E6 grand unified models with three
generations within the framework of Z12 asymmetric orbifold compactification of
the heterotic string theory. Such an asymmetric orbifold is missing in the
classification in the literature, which concludes that only one E6 model is
possible. In both of the new models, an adjoint Higgs field is obtained in
virtue of the diagonal embedding method. This method mods out the three E6
factors of an even self-dual momentum-lattice by a permutation symmetry. In
order to realize the E6^3 even self-dual lattice, we utilize the lattice
engineering technique. Among the eight possible orbifold actions in our setup,
two lead to new E6 models. Though these models still share the unsatisfactory
issues with the known one, our discovery raises hopes that excellent models
that solve all the problems in the supersymmetric grand unified models will be
found in this framework.
