Figure 17
are the ends of an edge e of a triangle T+ from the nesting determined by . At its midpoint z we see the edge of a triangle T from . The black triangles all come from the triangulation of , the largest ones being of level 3. The edge e is maximal, in the sense that it is not part of an edge of some larger triangle from . Thus, at its ends, the stripes of the large hexagons at v and are in the directions of the other sides of T+. The inner hexagons along are centered at double hexagon centers and their stripes are all oriented in the same direction, namely perpendicular to . At the left we have separated out the outer hexagons that overlay the small hexagons along . We see their matching arrows and how their stripes align to form the edge (in green). The colors (red/blue) of the short diameters of these large hexagons are determined by (or determine, whichever way one wants to put it) the color rule that we see in Fig. 10 , though note that the stripe of the large hexagons is perpendicular to that of the small ones, so the right/left crossing rule is opposite! The fact that the stripe orientation changes at the end dictates that the edge is an interior edge of a larger triangle. The shift indicated by the orientation of the arrows matches this. |