Geodesic
Hegaard diagrams and colored polyhedra
Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part II, Tome 66 (1976), pp. 180-188 
M. L. Starets. Hegaard diagrams and colored polyhedra. Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part II, Tome 66 (1976), pp. 180-188. http://geodesic.mathdoc.fr/item/ZNSL_1976_66_a8/
@article{ZNSL_1976_66_a8,
     author = {M. L. Starets},
     title = {Hegaard diagrams and colored polyhedra},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {180--188},
     year = {1976},
     volume = {66},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_66_a8/}
}
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%J Zapiski Nauchnykh Seminarov POMI
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.