Convex 3-polytopes with exactly two types of edges
Abstract We consider convex 3-polytopes with exactly two types of edges. The questions of the existence of such 3-polytopes are solved. The cardinalities of all classes are determined.
On quadrangular convex 3-polytopes with at most two types of edges
The type of an edge e in a quadrangular 3-polytope is the pair of valences of the end-vertices of e . To every two valence pairs U , V the cardinality of the family of quadrangular 3-polytopes whose all edges have type U or V is determined.
Brauer groups of genus zero extensions of number fields
We determine the isomorphism class of the Brauer groups of certain nonrational genus zero extensions of number fields. In particular, for all genus zero extensions E of the rational numbers Q that are split by Q(√2), Br(E) ≅ Br(Q(t)).