Granny knot

The knots in Figure 21 are all prime knots because they cannot be divided (factored) into smaller, nontrivial knots. Prime knots are the building blocks of composite knots and of links. Like prime numbers, which yield composite numbers upon multiplication, or like atoms in chemistry, which yield molecules upon combination, prime knots are the elementary units of knot theory. Composite knots are exemplified by the topologically achiral square knot and the topologically chiral granny knot (Figure 22). In each of these knots, a plane perpendicular to the... 

Figure 22. Diagrams of composite knots with c(K) = 6. (a) Square, or reef knot, (b) and (c) Enantiomorphs of the granny knot.

Pig. 11.1 Several simple knots. For the trefoil knot 3i, two isomers are shown, they are mirror impages of one another. Also, two distinct composite knots are shown (called granny and square), combining different trefoil isomers. 

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