  We study a family of frustrated anti-ferromagnetic spin-$S$ systems with a
fully dimerized ground state. This state can be exactly obtained without the
need to include any additional three-body interaction in the model. The
simplest members of the family can be used as a building block to generate more
complex geometries like spin tubes with a fully dimerized ground state. After
present some numerical results about the phase diagram of these systems, we
show that the ground state is robust against the inclusion of weak disorder in
the couplings as well as several kinds of perturbations, allowing to study some
other interesting models as a perturbative expansion of the exact one. A
discussion on how to determine the dimerization region in terms of quantum
information estimators is also presented. Finally, we explore the relation of
these results with a the case of the a 4-leg spin tube which recently was
proposed as the model for the description of the compound
Cu$_2$Cl$_4$D$_8$C$_4$SO$_2$, delimiting the region of the parameter space
where this model presents dimerization in its ground state.
