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Figure 8
v is a vertex of a triangle (shown in black) of level k. At v there is a small hexagon and its stripe allows for only two things to happen: either one of the edges of the triangle extends through v, in which case it is an edge from a larger triangle, or there is an edge passing through v that is parallel to the opposite edge of the triangle. In the latter case we use (i) of proposition 4.1[link] to place down the two opposite pairs of triangles of adjoining triangles, shown in green (the adjacent edges are actually coincident edges of course). Then we see that the edge through v must actually be an edge that includes both the top edges of the green triangles: thus again a larger triangle.

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ISSN: 2053-2733
Volume 73| Part 3| May 2017| Pages 246-256
https://doi.org/10.1107/S2053273317003576
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