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Original Articles

THE ENERGETIC STABILITY OF TORI AND SINGLE-WALL TUBES

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Pages 445-465 | Received 26 Apr 2001, Published online: 19 Aug 2006

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  • Note: A toroidal polyhex can be defined by three numbers, a,b,d. The closed toroidal network is mapped onto an infinite planar tiling with hexagons, giving a biperiodic pattern. If one of the hexagons is labelled, then the positions where it repeats will enable one or more polyhex parallelograms to be outlined which represent the whole set of hexagons on the torus. From one of these markers, count hexagons until the label repeats itself at the ath hexagon; return to the origin and count along the same row until, at the bth hexagon, there is a repeat marker at 120 degrees to the forward direction; count up this diagonal until this last marker is found at the dth hexagon. In general there are up to six possible a,b,d, triplets. The convention for choosing a canonical code is to choose one with minimum d, and from these, the one with minimum b
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