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HEXAGONAL
LUNDA
DESIGNS




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Figure 33: Examples of hexagonal grids.

Another way to expand the concept of Lunda-design is to start with hexagonal grids instead of rectangular ones. Figure 33 displays two examples.


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Figure 34.

Each grid point is surrounded by six unit triangles. Each border unit triangle has three unit triangles that touch the border (see Figure 34a), and between two arbitrary neighbouring grid points, there is always a hexagon composed of six unit triangles (see Figure 34b). Suppose that to each unit triangle of a hexagonal grid we assign one of three colours (e.g. white, grey, and black). Then we obtain a three-coloured design. If such a design satisfies the following two conditions:

  • (i) To the three border unit triangles of any border grid point different colours are assigned;
  • (ii) Of the six unit triangles between two arbitrary neighbouring grid points, there are two of each colour,
    we call it a hexagonal Lunda-design. Properties (i) and (ii) guarantee local equilibria between the three colours.



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    Figure 35.

    Figure 35b shows an example of a hexagonal Lunda-design.


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    Figure 36.


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    Figure 37.

    Figure 36 presents seven hexagonal Lunda-designs that have a three-colour rotational symmetry: a 60 rotation about the centre is consistent with colour. A clockwise rotation by 60 moves all the white to coincide with all the grey, moves grey to black, and black to white. In other words, the three colours occupy equivalent parts of the design. In the case of the four hexagonal Lunda-designs in Figure 37, a clockwise rotation by 120 moves white to grey, grey to black, and black to white.


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