Geodesic
Some news about oblique graphs
Discussiones Mathematicae. Graph Theory, Tome 22 (2002) no. 1, pp. 39-50

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A k-gon α of a polyhedral graph G(V,E,F) is of type 〈b₁,b₂,...,bₖ〉 if the vertices incident with α in cyclic order have degrees b₁,b₂,...,bₖ and 〈b₁,b₂,...,bₖ〉 is the lexicographic minimum of all such sequences available for α. A polyhedral graph G is oblique if it has no two faces of the same type. Among others it is shown that an oblique graph contains vertices of degree 3. 
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Dobrynin, Andrey; Melnikov, Leonid; Schreyer, Jens; Walther, Hansjoachim. Some news about oblique graphs. Discussiones Mathematicae. Graph Theory, Tome 22 (2002) no. 1, pp. 39-50. http://geodesic.mathdoc.fr/item/DMGT_2002_22_1_a4/