  We demonstrate that it is possible to produce different isotropic embeddings
of anisotropic Loop Quantum Cosmology, resulting to "lattice refinement" in the
isotropic system. To introduce the general approach, we first use a simple
model with only two anisotropic directions. We then employ the specific case of
a Bianchi I model, to show how the method extends to three-dimensional systems.
To concisely calculate the step-size of the resulting isotropic state, we
define the "symmetric dual" of states and operators, for the two- and
three-dimensional systems, respectively.
