  Here we consider the Ising-Heisenberg model in the expanded Kagom\'e lattice,
also known as triangle-dodecagon (3-12) or star lattice. This model can still
be understood as a decorated honeycomb lattice. Assuming that the Heisenberg
spins are at the vertices of the triangle while other spins are of the Ising
type. Thus, this model is equivalent to an effective Kagom\'e Ising lattice,
through the decoration transformation technique. Thus this means that the model
is exactly solvable so we can study the most relevant properties of this model.
Like the phase diagram at zero temperature, exhibiting a frustrated phase, a
ferromagnetic phase, a classical ferrimagnetic phase and a quantum
ferrimagnetic phase. We observed that Heisenberg spin exchange interaction
influences the frustrated phase, but we rigorously verify that the magnitude
and origin of the frustration emerge in a similar way to antiferromagnetic
Ising Kagom\'e lattice. Likewise, the thermodynamic properties of the model can
also be obtained, such as the critical temperature as a dependence of the
Hamiltonian parameters and the spontaneous magnetization of the model. Besides,
we investigated the entropy of the model, identifying its residual entropy in
the frustrated region. Even we analyze the specific heat behavior as a
temperature dependence, to deal with the phase transition.
