Fabric techniques (continued)

Many fabric techniques can be represented by a pair of generic quadrilateral truchet tiles. The single yarn that makes the fabric passes through each tile twice. Each time it passes through, it enters and exits through adjacent edges of the quadrilateral. Each edge of the quadrilateral plays a unique role as either the entrance, or the exit of either the first, or the second pass.

A nice property of orientable surfaces is that these two sequential passes are always countercurrent (even in high genus surfaces.) That, together with the fact that we need to color the first and second passes differently, means we need two generic truchet tiles that are mirror images of each other.

In the pair of generic truchet tiles shown here, the first pass is shown bright white, the later pass is colored faded gray.

In almost every technique, not much happens on the first pass: a loop of yarn is simply left behind for the second pass to seize upon. An asymmetrical teardrop shape is used in these two tiles to indicate a generic fabric technique that accomplishes most of its work on the second pass.