Lines and Edges

The large set of patterns in Chap. 9 had the property edge-to-edge. This is the usual case, but there are exceptions (one example was shown in Fig. 5.3). Further examples arise when a tile is not even a topological disc, but has a ‘hole’ as shown by the red tile in Fig. 11.1c. We call this a chelate. The ‘hole’ is actually a small polygon (wholly within another polygon) which always seems to be a kite. Three examples are shown in Fig. 11.1. (Note that Fig. 11.1a has a similar arrangement as Fig. 14.5a.) All the examples here come from Cairo, and no example is known from the Maghreb. In spite of this irregularity, all the three figures could be coloured with just two colours.