  In this article, we discuss the quasiconformal structure of boundaries of
right-angled hyperbolic buildings using combinatorial tools. In particular we
exhibit some examples of buildings of dimension 3 and 4 whose boundaries
satisfy the combinatorial Loewner property. This property is a weak version of
the Loewner property. This is motivated by the fact that the quasiconformal
structure of the boundary led to many results of rigidity in hyperbolic spaces
since G.D. Mostow. In the case of buildings of dimension 2, many work have been
done by M. Bourdon and H. Pajot. In particular, the Loewner property on the
boundary permitted them to prove the quasi-isometry rigidity of right-angled
Fuchsian buildings.
