Geodesic
On~the structure of~faces of~three-dimensional polytopes
Izvestiya. Mathematics , Tome 69 (2005) no. 4, pp. 847-864

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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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     author = {M. I. Shtogrin},
     title = {On~the structure of~faces of~three-dimensional polytopes},
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     volume = {69},
     number = {4},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2005_69_4_a8/}
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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/