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Figure 17
[v,v^{{\prime}}] are the ends of an edge e of a triangle T+ from the nesting determined by [{\cal T}^{{+}}({\bf r})]. At its midpoint z we see the edge [u,u^{{\prime}}] of a triangle T from [{\cal T}({\bf q})]. The black triangles all come from the triangulation of [{\cal T}({\bf q})], 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 [{\cal T}^{{+}}({\bf r})]. Thus, at its ends, the stripes of the large hexagons at v and [v^{{\prime}}] are in the directions of the other sides of T+. The inner hexagons along [vv^{{\prime}}] are centered at double hexagon centers and their stripes are all oriented in the same direction, namely perpendicular to [vv^{{\prime}}]. At the left we have separated out the outer hexagons that overlay the small hexagons along [vv^{{\prime}}]. We see their matching arrows and how their stripes align to form the edge [vv^{{\prime}}] (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[link], 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 [vv^{{\prime}}] is an interior edge of a larger triangle. The shift indicated by the orientation of the arrows matches this.

ISSN: 2053-2733
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