2. Weave Patterns

2.1. Tilings and Weave Patterns. When we look at the Archimedean tilings [1] we see that there are four tilings which can be colored in the way described above. Two of them, (4.4.4.4) and (3.6.3.6) are the underlying patterns of most of the weavings used in fabrics and baskets. The weaving derived from (4.4.4.4) is known as the plain weave (Figure 5), and the other as the three way weave (Figure 6).
Figure 5a: Tiling 4.4.4.4
Figure 5b: Plain Weave
Figure 6a: Tiling 3.6.3.6
Figure 6b: Three way weave
2.2. Closed Loops. The third Archimedean tiling that can be colored like a checkerboard is (3.4.6.4) (Figure 7a). The weaving derived from this tiling is that it is a weaving with closed loops (Figure 7b).
Figure 7a: Lines
Figure 7b: Weaving
The last one, tiling (3.3.3.3.3.3), can be colored in the right way but can not be transformed into a weaving pattern because the degree of each vertex is not four but six.