Figure 3
Embeddings, around a yellow cylinder, of the three isonemal nine-ring Borromean patterns. B(9,9)-a and B(9,9)-b have [vertex edge ring] transitivity [2 2 1], with 4-rings, and were reported earlier. Top row: projected down the ninefold axis (threefold if we factor in the coloring). Bottom row: normal to that axis. The red, blue and green triplets are internally Borromean in each case. B*(9,9)-c requires transitivity [3 3 1], and therefore has 6-rings to avoid intersecting edges, and forms a Borromean triplet of Borromean triplets, with R > G > B > R and (for the blue rings, right column) dark blue > medium blue > light blue > dark blue. Similarly, for the red and green rings. |