  In short geometrization conjecture of W.\,Thurston (finally proved by
G.~Perelman) says that any oriented $3$-manifold can be canonically partitioned
into pieces, which have a geometric structure of one of the eight types. In the
seminal paper (1991) M.\,W.\,Davis and T.\,Januszkiewicz introduced a wide
class of $n$-dimensional manifolds -- small covers over simple $n$-polytopes.
We give a complete answer to the following problem: to build an explicit
canonical decomposition for any orientable $3$-manifold defined by a
vector-colouring of a simple $3$-polytope, in particular for a small cover. The
proof is based on analysis of results in this direction obtained before by
different authors.
