1.1 Popular Lacings 3

Figure 1.4. Representatives of six popular families of lacings: the crisscross, zigzag, star,

bowtie, serpent, and zigsag lacings.

These lacings will play important roles in the following chapters, and it may

therefore be a good idea to memorize them right

now.1

Of course, the crisscross and the zigzag lacings are by far the most popular

lacings today. Therefore, we will also refer to them as the classical lacings.

The crisscross, zigzag, and star n-lacings exist for all n. For n = 2 these three

types of n-lacings coincide. For n 2 there is a unique crisscross n-lacing, two

zigzag n-lacings, and two star n-lacings. The two zigzag n-lacings are vertical mirror

images of each other. Similarly, the two star n-lacings are vertical mirror images of

each other. In all three cases, it should be clear from the diagrams how to construct

their n-lacing representatives.

Figure 1.5 shows the basic building blocks of the bowtie lacings. From left to

right, we have an end, a cross, and a gap. Here, an end is a horizontal that connects

either the top two or the bottom two eyelets. This means that a lacing contains at

most two ends. A cross consists of two 1-diagonals that are situated with respect to

each other as shown in the middle diagram. Finally, a gap consists of two 1-verticals

that are situated with respect to each as shown in the right-hand diagram.

Figure 1.5. The basic building blocks of the bowtie lacings.

Clearly, the crisscross n-lacing is made up of the two ends and n-1 crosses. An

n-lacing is a bowtie n-lacing if it is made up of two ends and

• n/2 - 1 crosses and n/2 gaps if n is even, and

• (n - 1)/2 crosses and (n - 1)/2 gaps if n is odd.

1 To facilitate memorization, we have chosen names that capture the construction prin-

ciples behind the different lacings: (1) crisscross–note all the crosses in the middle of

these lacings; (2) zigzag–discard the long segment and you end up with a long zigzag;

(3) star–note the partial Stars of David that are hiding in these lacings; (4) bowtie–turn

this bowtie 6-lacing 90 degrees and you see a bowtie; (5) serpent–this lacing winds left

and right like a serpent; (6) zigsag–reminiscent of zigzag lacings.