the boundary of the polygon clockwise (with your right hand inside the polygon and your left hand outside). At a convex corner, you turn 90° right; at any concave corner, you turn 90° left. Finally you must make an entire 360° turn and come back to the original point; hence the number of right turns must be 4 more than the number of left turns. Corollary: every rectilinear polygon has at least 4 convex corners. The number of knobs (sides connecting two convex corners) is four more than the number of antiknobs (sides connecting two concave corners).To see why, let X be the number of convex corners and Y the number of concave corners. By the previous fact, X=Y+4. Let XX the number of convex corners followed by a convex corner, XY the number of convex corners followed by a concave corner, YX and YY defined analogously. Then obviously X=XX+XY=XX+YX and Y=XY+YY=YX+YY. Hence XX=X-XY=X-(Y-YY)=YY+(X-Y)=YY+4. Corollary: every rectilinear polygon has at least 4 knobs. Squares and rectangles in a rectilinear polygon A rectilinear polygon can be covered by a finite number of squares or rectangles with edges parallel to the edges of the polygon (see Polygon covering). It is possible to distinguish several types of squares/rectangles contained in a certain rectilinear polygon P: A maximal square in a polygon P is a square in P which is not contained in any other square in P. Similarly, a maximal rectangle is a rectangle not contained in any other rectangle in P. A square s is maximal in P if each pair of adjacent edges of s intersects the boundary of P. The proof of both sides is by contradiction: If a certain adjacent pair in s does not intersect the boundary of P, then this pair be pushed further towards the boundary, so s is not maximal. If s is not maximal in P, then there is a larger square in P containing s; the interior of this larger square contains a pair of adjacent edges of s, hence this pair does not intersect the boundary of P. The first direction is also true for rectangles, i.e.: If a rectangle s is maximal, then each pair of adjacent edges of s intersects the boundary of P. The second direction is not necessarily true: a rectangle can intersect the boundary of P in even 3 adjacent sides and still not be maximal as