Areas of generalized H-polygons

摘要

Let H be the set of vertices of a tiling of the plane by regular hexagons of unit area. There is a Pick-type formula which can be applied only to a restricted class of polygons with corners in H. The main purpose of the paper is to give a Pick-type formula applicable to arbitrary H-polygons. The setting is that of general oriented polygons as introduced by Grunbaum and Shephard. (C) 1997 Academic Press.