Some of the 3 string knots (that is knots built from an interweave of 3 smaller knots) allow braiding three pass "gaucho" type knots with single pass locked edges. They also produce some unique color patterns that are fairly symetrical.
We begin this knot by laying a 5 X 4 sobre simple turkshead on a twelve pin mandrel using the bight increment for the 15 part finished knot. This template is from a perspective of beginning at the lower right corner and finishing at the lower left corner. There is no good place for the last "tuck up" yet so leave the running end and standing end crossed with enough extra for the finish later.
With the template rotated 90 degrees clockwise, lay in the second section exactly parallel to the first for another complete 5 X 4 knot identical to the first. At the end of each path across the knot, be careful to leave a little bit of slack so that the new lead does not pull down behind the cross in the first knot here. The third knot will pass through this space and lock the edges of the finished knot. You may notice that this is strictly an under two over two - - structure.
The third pass now just follows the code sequence of under one-over three-under three-over three-under three-over one, counting the vacant spaces in the lattice as well as leads crossed in both directions across the knot. You might also notice that each transition from under to over and from over to under splits a parallel pair between the second and first knot and you only pass three strings when one of them is the standing end of the third knot.
The template at the left is the same knot with all three strings the same color. Of course this same knot with one less bight could been done with a single string, but not this simply.
The second template is done with two strings of one color and a third of a contrasting color for a unique color pattern. It is also done with 21 parts ( three 7X4 base knots) by the same method as above. I will get to the matter of the various size knots this technique works for in a moment.
The first requirement for a three string knot is that the parts and bights both have a single common divisor of 3 and not be equal.
The only restraint on the number of bights is that it be divisible by 3 and not equal to the number of parts.
The number of parts must support the braid structure of one at the bottom and one at the top plus an even number of three pass sections. As each part crosses the remainder of the parts in each half wrap we need one more part than code passes in each. This results in a 9 part minimum for this interweave. It may be increased in increments of 6 for 9, 15, 21, 27 etc parts.This limits the range of possible knots somewhat.
The base or partial knots for this interweave are the result of dividing both the parts and bights of the completed knot by 3. Thus a 21 X 12 knot is built from three 7 part by 4 bight base knots.
However we place each of these on a 12 bight mandrel using the increments for the complete 21 parts, (10 and 1/2 pins for the first half wrap and 21 pins for the rest as for any simple turkshead of 21 parts. Of course the same method is used for any possible knot of this kind. The result is always a bight increment of three pins but the bight progression can be either CW or CCW depending on the ratio of parts to bights. This has no real effect on the final structure of the finished knot as the second and third knots are placed adjacent to the one before.
Copyright by Sidney Wood 07-07-08