Hegaard diagrams and colored polyhedra

The main result is a construction, which transforms an irreducible Hegaard diagram of genus $h$ of a closed three-dimensional manifold into a colored polyhedron with $2h$ faces, which determines the manifold. It is also shown that for any irreducible manifold of genus $h$ there exists a polyhedron with $2h$ faces, for which the factorization map is an immersion. An algorithm similar to Neuwirth's algorithm is constructed.