  We introduce an explicit combinatorial characterization of the minimal model
${\cal O}_{\infty}$ of the coloured operad ${\cal O}$ encoding non-symmetric
operads. In our description of ${\cal O}_{\infty}$, the spaces of operations
are defined in terms of hypergraph polytopes and the composition structure
generalizes the one of the $A_{\infty}$-operad. As further generalizations of
this construction, we present a combinatorial description of the
$W$-construction applied on ${\cal O}$, as well as of the minimal model of the
coloured operad ${\cal C}$ encoding non-symmetric cyclic operads.
