Geodesic
On the structure of faces of three-dimensional polytopes
Izvestiya. Mathematics, Tome 69 (2005) no. 4, pp. 847-864 
M. I. Shtogrin. On the structure of faces of three-dimensional polytopes. Izvestiya. Mathematics, Tome 69 (2005) no. 4, pp. 847-864. http://geodesic.mathdoc.fr/item/IM2_2005_69_4_a8/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In Euclidean three-space, we consider two-dimensional polyhedra that are homeomorphic to closed surfaces. The structure of an arbitrary face of such a polyhedron is studied in detail. In particular, we prove the following main theorem. If a two-dimensional polyhedron lies in Euclidean three-space and is isometric to the surface of a convex three-dimensional polytope, then all the faces of the polyhedron are convex polygons.

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