Among the smallest knotted (unicursal or single-cycle) kagome baskets are some elongated small-diameter shapes reminiscent of carbon nanotubes. Shown above is the medial graph of Plantri 15-253174, which has the following road code: 10.17 4.21 24.1 27.6 31.12 14.33 8.37 2.41 42.23 43.0 25.44 46.39 48.19 29.50 52.35 54.15 32.55 13.56 57.34 53.58 59.16 11.60 30.61 51.62 63.36 9.64 65.18 49.66 28.67 7.68 69.38 47.70 71.20 5.72 26.73 45.74 75.40 3.76 77.22
This shape can be lengthened 6 vertices at a time. Its shorter predecessor is Plantri 9-12 of the previous post. The endcaps in both baskets are the same, the middle section, which in the 3-regular Tait graph is all hexagonal faces, gets longer 6 hexagons at a time. In carbon chemistry this would be a non-classical fullerene since each end cap has 1 triangular, 1 square, and 1 pentagon face. The face histogram for the 3-regular graph is [0 0 0 2 2 2 9].
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