3.1. Connecting intersection points. Each tiling can be used to create a new tiling that can be colored as a checkerboard. When we add the dual pattern to an existing pattern we will get intersection points between both patterns. Each of those points lays on a line which is the edge of two adjacent tiles. On both tiles this edge is connected to exactly two other edges, on which there are also intersection points. So we have four direct neighbour points for each intersection point. Connecting each intersection point to the four direct neighbour points will thus give us a graph in which each vertex has degree four. So we will get a tiling which can be colored as a checkerboard, that can be used as an underlying pattern for a weaving. In Figure 9 you can see the result of this process applied on the Archimedean tiling (3.3.4.3.4) (Figure 8a).
This operation corresponds to the “ambo” operation that is part of Conway Polyhedron notation [2].