3.3. Dual Tiling Patterns. Besides the four Archimedean patterns we have discussed so far, there are no patterns with tiles with a maximum of five edges. But we can create more basic patterns by making the dual patterns of the Archimedean patterns, as is shown in Figure 22 for the pattern 33434.
Figure 22: Creating the dual pattern of tiling pattern 33434.
And now this pattern with pentagonal tiles can be used to make the elevation (Figure23).
Figure 23: Model of the elevation.
All patterns dual to the Archimedean patterns, except 333333, have tiles with a maximum of 5 edges. In Figures 24 and 25 the process is shown starting with the Archimedean tilings 488 and 3636. In both cases the double woven elevation technique, as described in Section 2.2, is applied.
Figure 24abc: Creating the dual pattern of tiling pattern 488.
Figure 24de: Double woven elevation structure.
Figure 25abc: Creating the dual pattern of tiling pattern 3636.
Figure 25de: Double woven elevation structure.