**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. |