Specifying the staircase kernel of a two-fold connected orthogonal polygon

Abstract

Let S = φ be a two-fold connected orthogonal polygon in the plane. Assume that S is starshaped via staircase paths and K is any component of KerS, the staircase kernel of S. Let B be the bounded component of R 2 \S. If B contains one kind of north, east, south and west dents then KerS is either one component or two and the positions of these components agree with the kind of dents. But if B contains two kinds of north, east, south and west dents then either K er S is one component or S is not starshaped via staircase paths.