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periodic lattice component

Figure 4: T2 crystallizes in two forms. Left: diagonally nested. Right: stacked in vertical columns, for which only one relative alignment is possible. The enantiomorphic stacking in rows is geometrically possible for triangles as such, but would run counter to the prohibition of contiguous top margins for evolutionary reasons.
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There are two prime cycles for T2, consisting exclusively of T2's which are stacked diagonally in the first cycle of length 8, and vertically in the second cycle of length 9. There are no alternatives, but larger composites may arise when the shift period coincides with other designs.


Table 2: multiples of the unit cell for diagonal stacking are marked d, for columnar stacking by c. Where other designs have coincidental shift periods, the mark is x.
  10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10
1 . . . . c . . d . . . . . c . d . . . . .
2 . . . . d . . . . . . . d . . . c . . . d
3 . x . . . . . . . d . . . . . . . d . c .
4 . . . . c . d . . . . . . c d . . . . . .
5 . . . d . . . . . . . d . . . . c . . d .
6 d c . . . . . . d . . . . . . . d . . c .
7 . . . . c d . . . . . . . x . . . . . . .
8 . . d . . . . . . . d . . . . . c . d . .
9 . c . . . . . d . . . . . . . d . . . c .
10 . . . . x . . . . . . . d c . . . . . . d



next up previous contents
Next: T3 Up: T2 Previous: cross references   Contents
Jose Manuel Gomez Soto 2002-05-15