Covering the Plane with Convex Polygons.
This paper describes local configurations of some planar triangulations. A Gauss-Bonnet-like formula holds locally for a kind of discrete “curvature” associated to such triangulations.
Let and be two groups of finite order , and suppose that they share a normal subgroup such that if or . Cases when is cyclic or dihedral and when for exactly pairs have been shown to be of crucial importance when studying pairs of 2-groups with the latter property. In such cases one can describe two general constructions how to get all possible from a given . The constructions, denoted by and , respectively, depend on a coset (or two cosets and ) modulo , and on an...