A. O. Ivanova

Describing edges in triangle-free 3-polytopes

An edge e in a 3-polytope is of type ( k 1 , k 2 , k 3 , k 4 ) if the set of degrees of the vertices and faces incident with e is majorized by the vector ( k 1 , k 2 , k 3 , k 4 ) . In 1940, Lebesgue proved that every 3-polytope has an edge of one of the types ( 3 , 3 , 3 , ∞ ) ,...