Novel Braid Design

Index

Preface Flat Braids

No:

1

Round Braids

No:

10

Asymmetrical Round Braids

No:

24

Braids with Reversals and Twists

No:

31

Two Cells Thick Braids

No:

40

About Cells

No:

53

Diagram-Method

No:

55

Reversed-Diagram-Method

No:

60

Designing a Block Braid

No:

62

Three or More Cells Thick Braids

No:

67

Multiple Cells Round Braids

No:

75

Linked Braids

No:

80

Braids with Edge Effect

No:

97

Bonus

No: 106

Preface

At regular moments I find myself braiding. Not so much the end result, but rather understanding what makes braids tick and designing new braids continues to fascinate me.

This is a selection of different braids I have designed over time. I’ve also put various ideas and methods on paper, which help me design new braids. It is however not necessary to read this theory, with the instructions at the beginning of the chapters about flat and round braiding it is possible to make almost every braid directly by just following the Braid Tables.

I have limited myself to braiding by hand, so without tools such as braid cards or tables.

And secondly, they are flat braids; they are braided in a two-dimensional plane. However, this has hardly proved to be a limitation, as evidenced by the wide variety of designs and the many possibilities I still foresee.

A final remark: I want to share this information freely with all people interested. Therefore, this is a free public domain book with no copyright. I hope this collection will give you a lot of pleasure, relaxation and inspiration.

Paulus, March 2013

Flat Braids No: 1 – Five Strand Flat Braid First, here is an explanation of flat braiding using a 5-strand braid.

– Tie five strands together at the top and attach to a fixed point.

– Divide the strands into two flat bundles, 3 strands on the left, 2 strands on the right.

– Take the left bundle in the left hand, the right bundle in the right hand.

– Give each strand a number or letter 1) Step 1: – Move the left strand of the left hand (strand 1) over strand 2, under strand 3, then place it on the left side of the right bundle: position (c).

– The strands are renamed to the starting position. The left strand in the left hand, formerly number “2”, now gets number "1", etc. Please note; this renumbering happens after every braiding step.

Step 2:– Bring the right strand (strand a) over strand b, under strand c, and place it on the right side of the left bundle: position (3).

- Renumber.

- Repeat steps 1 and 2 until the braid has the desired length.

1)

The strands receive a number or letter, depending on the position of the strand. This is shown in the drawing: the left-hand strand in the left hand is given the number “1”, the one next to it number “2”, etc. Similarly, the right-hand strand in the right hand is given the letter “a”, the next the letter “b ”, Etc. The next free position next to each bundle is indicated by a number or letter in brackets, in this case (c) and (3).

Flat Braids In a Table this looks like this:

Table 1

1

2

3

c

1 (3L/2R)

^

2

-

*

*

-

2 (2L/3R)

b

a

b

^

Each table-row is a braiding step. The first column shows the step number and between brackets the number of strands in left- and right hand at the start of that braiding step.

The symbol “^” indicates which strand is handled; the “active” strand. When there is a number or letter in a box, this means the active strand crosses over that strand. When there is an “-“ in a box, the active strand crosses under that strand. The symbol "*" indicates where the active strand is placed at the end of that braiding step.

The last part is the Diagram: the green drawing. This represents the cross section of the braid. The lines indicate the paths along which the strands of the braid move. This will hopefully become clearer further on in this book.

The Table is a simple but important part of this book. When you can read the Table, you can make almost all the braids in this book (only those in the "Braids with Edge Effect" section require some extra technique). The basis of the table has now been described, further on a few more moves are added: -

The technique of Round Braiding: No: 10, Symbols above the table for strands in the same track: No: 32, The letters "L" and "R" for a Twist: No: 36 and 37, The letter "S" for a Swap: No: 109.

Flat Braids No: 2 – Ridge By having the strands cross over and under several strands at a certain place, the braid shows a thickening at that place. This can be done along the edges such as the following braid.

Table 2

1

2

3

4

d

1 (4L/3R)

^

2

3

4

*

*

d

2 (3L/4R)

c

b

a

c

b

^

Flat Braids No: 3 – Flat Braid with Herringbone Pattern At the first braid of this chapter, a strand always crosses over and under one strand. For the next 9-strand braid, each strand crosses over 2 strands and then under 2 strands. The crossings of this braid lie much closer to each other than the previous braid and the result is much more compact. This pattern is called a herringbone.

Table 3

1

2

3

4

5

e

1 (5L/4R)

^

2

3

-

-

*

*

-

2 (4L/5R)

d

c

b

a

-

c

b

^

Flat Braids No: 4 – Flat Braid with Even Number of Strands Flat braids are often made with an odd number of strands but are just as easy to make with an even number of strands. This is a braid with an even number of strands and a thickened centre.

Table 4

1

2

3

d

1 (3L/3R)

^

2

-

*

*

d

2 (2L/4R)

c

b

a

c

-

^

Flat Braids No: 5 - Asymmetrical Braid Many patterns are possible, the greater the number of strands, the more options. The design of a braid does not have to be symmetrical. This is an asymmetrical example.

Table 5

1

2

3

4

5

c

1 (5L/2R)

^

-

-

-

5

*

*

c

2 (4L/3R)

b

a

-

^

Flat Braids No: 6 – Double Bar In the middle of the following design, the strands run in pairs over each other. Because the pattern is repeated in the longitudinal direction after 4 rows of crossings, 4 braid steps are required.

Table 6

1

2

3

4

e

1 (4L/4R)

^

-

3

-

*

*

e

4

*

*

e

2 (3L/5R) 3 (4L/4R) 4 (3L/5R)

^

-

3

d

c

b

a

d

-

b

^

-

-

b

^

Flat Braids No: 7 - Wickerwork An elegant continuation of the previous braid is this "Twill" braid.

Table 7

1

2

3

4

5

f

1 (5L/5R)

^

2

3

-

-

*

*

-

-

*

*

f

2 (4L/6R) 3 (5L/5R) 4 (4L/6R)

^

2

3

-

e

d

c

b

a

-

-

c

b

^

-

-

c

b

^

Flat Braids No: 8 – Flat Bubbles The possibilities of flat braids are endless. Inspiration for this braid came from the round braid "Bubbles" (No: 14).

Table 8

1

2

3

4

5

6

g

1 (6L/6R)

^

-

3

4

-

-

*

*

g

6

*

*

-

2 (5L/7R) 3 (6L/6R) 4 (5L/7R)

^

2

-

-

-

f

e

d

c

b

a

f

-

-

-

b

^

-

-

d

c

-

^

Flat Braids No: 9 - Fake Here a special pattern to conclude this chapter. When you follow the steps neatly, the result looks like a fair braid. With a few firm jerks, however, it falls apart into two separate bundles. This braid comes from The Ashley Book of Knots, a great source of inspiration for me. For this braid with even number of strands, it was decided not to braid from alternating hands but to make two following steps with the same hand. This makes the left and right operations symmetrical which results in considerably easier braiding. I have not applied this principle further but you can use it with many more braids.

o

+

o

Table 9

1

2

3

1 (3L/1R)

^

2

3

2 (2L/2R)

^

2

x

3 (1L/3R) 4 (2L/2R)

* *

+ c

b

a

* * c

b

^

x

b

^

Round Braids No: 10 – Eight Strand Round Braid with Herringbone Pattern Making a round braid is done almost the same way as a flat braid. Here is the explanation of an 8-strand round braid with a herringbone pattern.

- Tie eight strands together at the top and attach at a fixed point.

- Divide the strands into two flat bundles, 4 strands on the left, 4 strands on the right.

- Take the left bundle in the left hand, the right bundle in the right hand.

- Name the strands (just like a flat braid No: 1).

Step 1:- Bring the left strand (strand 1) first downwards and then along the back, all the way to the right. Pass it under strand a and b, over strand c and d, and place it on the right side of the left bundle: position (5).

- Renumber Step 2:- First bring the right strand (strand a) down and then along the back, all the way to the left. Pass it under strand 1 and 2, over strand 3 and 4, and place it on the left side of the right bundle: position (e).

- Renumber - Repeat steps 1 and 2 until the braid has the desired length.

Round Braids In Table form this looks like this:

Table 10

1

1 (4L/4R)

^

2 (4L/4R)

-

2

-

3

3

4

4

d

c

b

a

d

c

-

-

on (5)

^

on (e)

“Round� refers more to the principle of braiding than the final form. In a Round Braid, the individual strands do not move back and forth within a braid but two groups of strands rotate in opposite directions. This braid has a square shape.

Round Braids No: 11 - Smoker Here follow eight examples of round braids with 8 strands. Eight strands fit nicely in your hands, offers many design options and will readily give a stable braid.

Table 11

1

1 (4L/4R)

^

2 (4L/4R)

1

3 (4L/4R)

^

4 (4L/4R)

-

2 2

3 -

4

d

c

b

a

d

-

-

a

on (5)

^

on (e)

-

on (5)

^

on (e)

-

2

3

4

-

b

Round Braids No: 12 – 22/13

Table 12

1

1 (4L/4R)

^

2 (4L/4R)

-

3 (4L/4R)

^

4 (4L/4R)

-

2 2

3 3

4

d

c

b

a

d

c

-

-

on (5)

^

on (e)

a

on (5)

^

on (e)

d

-

3

4

-

-

Round Braids No: 13 - Randevou

Table 13

1

1 (4L/4R)

^

2 (4L/4R)

1

3 (4L/4R)

^

4 (4L/4R)

1

2

-

3

3

4

d

c

b

a

d

c

-

-

on (5)

^

on (e)

a

on (5)

^

on (e)

4 d

2

-

-

-

b

Round Braids No: 14 – Bubbles

Table 14

1

1 (4L/4R)

^

2 (4L/4R)

1

3 (4L/4R)

^

4 (4L/4R)

1

2

-

3

-

4

d

c

b

a

d

c

-

-

on (5)

^

on (e)

a

on (5)

^

on (e)

4 d

2

-

-

-

-

Round Braids No: 15 – Tic-Tac

Table 15

1

1 (4L/4R)

^

2 (4L/4R)

-

3 (4L/4R)

^

4 (4L/4R)

-

2

-

3

3

4

d

c

b

a

-

-

b

-

on (5)

^

on (e)

-

on (5)

^

on (e)

-

2

3

-

c

b

Round Braids No: 16 – Caught

Table 16

1

1 (4L/4R)

^

2 (4L/4R)

-

3 (4L/4R)

^

4 (4L/4R)

1

2

2

3

3

4

d

c

b

a

d

-

-

a

on (5)

^

on (e)

-

on (5)

^

on (e)

-

-

-

4

c

b

Round Braids No: 17 – Duplo

Table 17

1

1 (4L/4R)

^

2 (4L/4R)

1

3 (4L/4R)

^

4 (4L/4R)

1

2

-

3

-

4

d

c

b

a

d

c

b

-

on (5)

^

on (e)

a

on (5)

^

on (e)

4 d

2

3

-

-

-

Round Braids No: 18 - Spike Here is another nice round braid with 8 strands. The name came from the resemblance with a wheat head.

Table 18

1

1 (4L/4R)

^

2 (4L/4R)

-

3 (4L/4R)

^

4 (4L/4R)

-

5 (4L/4R)

^

6 (4L/4R)

-

2

-

3

-

4

d

c

b

a

d

-

-

-

on (5)

^

on (e)

-

on (5)

^

on (e)

-

on (5)

^

on (e)

4 d

-

3

3

-

4 d

2

c

4

c

b

Round Braids No: 19 – Peekaboo With the previous braids of 8 strands, the braid pattern repeats after 4 vertical columns of crossings so twice along the circumference of the braid. The possibilities expand considerably when the pattern is repeated after 8 columns. This means that with a braid of eight strands the pattern only occurs once. This one and the following are just three examples. The photo shows "front" and "back" side of the braid.

Table 19

1

1 (4L/4R)

^

2 (4L/4R)

1

3 (4L/4R)

^

4 (4L/4R)

-

2

-

3

3

4

d

c

b

a

d

c

-

-

on (5)

^

on (e)

a

on (5)

^

on (e)

4 d

3

4

-

-

b

Round Braids No: 20 – Slant Just like the previous, a braid pattern that occurs only once along the circumference of the braid.

Table 20

1

1 (4L/4R)

^

2 (4L/4R)

-

3 (4L/4R)

^

4 (4L/4R)

1

2

2

3

3

4

d

c

b

a

-

c

b

a

on (5)

^

on (e)

a

on (5)

^

on (e)

d

2

-

4

-

-

Round Braids No: 21 – Great Spike This braid is not very stable but is included because of its unusual pattern. I count the braiding steps while braiding so as not to lose the thread.

Table 21

1

1 (4L/4R)

^

2 (4L/4R)

-

3 (4L/4R)

^

4 (4L/4R)

-

5 (4L/4R)

^

6 (4L/4R)

1

7 (4L/4R)

^

8 (4L/4R)

1

9 (4L/4R)

^

10 (4L/4R)

-

2 -

3 -

4

d

c

b

a

d

-

b

a

on (5)

^

on (e)

a

on (5)

^

on (e)

-

on (5)

^

on (e)

-

on (5)

^

on (e)

-

on (5)

^

on (e)

4 d

-

-

-

-

-

4 d

-

-

4 d

-

-

4 d

2

-

4

-

-

Round Braids No: 22 - Spiral In the following design, the pattern shifts diagonally. The result is a braid with a beautiful spiral. The pattern is repeated in longitudinal direction after 10 rows of crossings. Normally, therefore, 10 braiding steps would be required. Braiding two times in succession with a strand from the right hand makes three steps sufficient. Give the braid the opportunity to turn during braiding to keep the pitch of the left and right group equal.

With every round braid you can choose alternative braiding steps within the Braid Scheme.

The left and right side of the column of crossings that you take with you in the braid steps must fit together, the braid pattern must continue. You can see this column as a cylinder whose sides connect at the back of the circular braid.

Table 22

1

2

3

4

1 (5L/5R)

^

2 (5L/5R)

-

2

-

-

3 (5L/5R)

-

-

3

-

5

e

d

c

b

a

e

d

c

-

-

on (6)

5

^

on (f)

5

^

on (f)

Round Braids No: 23 – Transition of Patterns By drawing out a Braid Scheme it is possible to make a transition from one braid pattern to the other. In the following example, a piece of braiding is included which consists of two separate 4-strand braiding over one another. Because this piece of braiding is incorporated in a stable 8-strand braid, all the strands remain in place. Choose the point of transition in the patterns carefully so that there are no strands that run over or under too many strands. Three is just about the maximum. Sometimes this is not immediately possible.

Then a transition piece of 1 or 2 rows is needed between the two patterns with carefully chosen crossings. See also No: 47 for a easier example.

Table 23

1

Herringbone (Repeat step 1 and 2 until desired length)

1 (4L/4R)

^

2 (4L/4R)

-

Transition piece

3 (4L/4R)

^

4 (4L/4R)

-

5 (4L/4R)

^

6 (4L/4R)

-

7 (4L/4R)

^

8 (4L/4R)

-

9 (4L/4R)

^

10 (4L/4R)

1

11 (4L/4R)

^

12 (4L/4R)

-

13 (4L/4R)

^

14 (4L/4R)

-

Braid over Braid (repeat step 7 t/m 10 a number of times) Transition piece Herringbone (repeat step 13 en 14 until desired length)

2 -

3 3

4

d

c

b

a

d

c

-

-

on (5)

^

on (e)

-

on (5)

^

on (e)

4 d

-

3

-

-

3

4

d 2

-

-

-

3

4

d d 2

3 3

c c -

b -

4 d

-

c

4

c

-

-

on (5)

^

on (e)

a

on (5)

^

on (e)

-

on (5)

^

on (e)

a

on (5)

^

on (e)

-

on (5)

^

on (e)

Asymmetrical Round Braids No: 24 – Flat Round Braid The circular braids from the previous chapter were all symmetrical. Symmetrical means an equal number of strands rotate left and right. The number of strands that turn left and right does not have to be the same but may differ. This will affects the cross-section of the braid. Flat, triangular and square shapes are possible. This simple braid has a flat crosssection.

Table 24

1

1 (4L/2R)

^

2 (4L/2R)

-

2

-

3

3

4

-

b

a

b

-

on (5)

^

on (c)

Asymmetrical Round Braids No: 25 – Triangle With the next braid, three strands turn to the right and six strands to the left. The result is a beautiful triangular braid.

Table 25

1

1 (6L/3R)

^

2 (6L/3R)

-

2

-

3

3

4

-

5

-

6

6

c

b

a

c

b

-

on (7)

^

on (d)

Asymmetrical Round Braids No: 26 – Large Triangle This is a continuation of the previous triangle where now three instead of two strands are jumped. This braid retains its shape somewhat difficult, so it is advisable to use cores. Use of cores is dealt with in more detail at No: 30.

Table 26

1

1 (9L/3R)

^

2 (9L/3R)

-

2

-

3

-

4

4

5

-

6

-

7

-

8

8

9

-

c

b

a

c

b

-

on (10)

^

on (d)

Asymmetrical Round Braids No: 27 – Two/Two Triangle I incorporated this braid because of the insight it can provide. Although all cells contain 2 strands, this asymmetrical braid has a triangular shape. This braid, just like No: 30, benefits from a 3-strand twisted core.

Table 27

1

1 (9L/3R)

^

2 (9L/3R)

1

2

-

3

-

4

4

5

5

6

-

7

-

8

8

9

9

c

b

a

c

b

-

on (10)

^

on (d)

Asymmetrical Round Braids No: 28 – Asymmetrical Herringbone Just like the previous braid, this braid is "food for thought". In the Braid Scheme I have added information for clarification and as an aid to draw asymmetrical diagrams. This asymmetrical design has a herringbone pattern as each strand crosses over 2 strands and then under 2 strands. Each strand crosses 5 + 3 = 8 strands in 1 tour.

Table 28

1

1 (5L/3R)

^

2 (5L/3R)

-

2

-

3

3

4

4

5

-

c

b

a

c

-

-

on (6)

^

on (d)

Asymmetrical Round Braids No: 29 – Asymmetrical Spiral This braid has a fetching design with spiral pattern. This braid needs a core, how to do this is explained at the next braid.

Table 29

1

1 (7L/3R)

^

2 (7L/3R)

-

3 (7L/3R)

^

4 (7L/3R)

-

2 2

3 -

4 -

5 -

6 6

7

c

b

a

-

b

a

on (8)

^

on (d)

-

on (8)

^

on (d)

c

-

-

4

-

-

-

b

Asymmetrical Round Braids No: 30 - Square with Core With this square braid there are so many strands in the outer circumference that the braid becomes "hollow" and no longer holds its shape properly. The shape only holds if a core is included in the braid. This can be done afterwards but also during braiding. This is fairly easy. The core is placed in the middle between the left and right bundles at the start and the strands twist around it during braiding. So the active strand moves under the core to the bundle on the other side. Then moves according the Table over and under the strands and then returns over the core to the inside of the bundle where it was started. I use three twisted strands for the core for this braid.

\

Table 30

1

1 (8L/4R)

^

2 (8L/4R)

-

2

-

3

3

4

-

5

-

6

6

7

-

8

-

d

c

b

a

-

c

b

-

on (9)

^

on (e)

Braids with Reversals and Twists No: 31 – Loop Until now, strands have only turned in direction at the edges of the braid. This chapter contains braids whose strands change direction within the pattern (a Reversal) and two strands that turn around each other with both changing directions (a Twist).

A technique of braiding that I do not cover is hand and finger loop braiding. This technique uses loops that are placed around the fingers or hands. Loop manipulations are great and make it possible to easily handle large numbers of strands and produce beautiful braids.

Because the strands are braided in loops or pairs, this produces characteristic patterns of paired strands. This braid has such a pattern but is braided in the "normal" way. Please note, with this and more braids in this chapter, the outer strand is not always the active strand. At steps 1 and 3 of this braid, the second outermost is the active strand!

Table 31

1

1 (6L/4R) 2 (5L/5R) 3 (4L/6R) 4 (5L/5R)

^

2

3

4

5

6

^

-

-

-

-

2

3

-

-

x

* *

f

e

d

c

b

a

* * -

-

-

-

^

x

-

-

c

b

^

Braids with Reversals and Twists No: 32 – Winglets On top of the Braid Table of this braid there is a new row of symbols. Similar symbols indicate the positions of strands that belong to the same tracks in step 1. In the Diagram these tracks can be recognized as closed lines. For the sake of clarity, these are given the colours red and blue in this Diagram. When you make a braid for the first time, it gives guidance to give different tracks different colours. It makes it easier to keep the strands in order. Furthermore, it is a good check that you have not made a mistake because every time you arrive at step 1 the strands must be in given positions. Finally, it often produces elegantly coloured braids.

Table 32

+

o

+

o

+

1

2

3

4

5

^

3

-

-

-

-

4

x

1 (5L/3R) 2 (4L/4R) 3 (3L/5R) 4 (4L/4R)

^

* *

e

d

+

o

+

c

b

a

* * -

-

c

^

x

d

-

-

^

Braids with Reversals and Twists No: 33 - Plop This braid with Reversals is made in a special way. Braiding is only done with the outer strands (strand 1 and a). However, after braiding the strands still have to be placed in the right place. The outer bends of a number of strands have to be moved inwards. It is difficult to explain, it is a matter of doing.

Table 33

1

2

3

d

1 (3L/3R)

^

-

3

*

*

-

-

*

*

-

2 (2L/4R) 3 (3L/3R) 4 (2L/4R)

^

-

c

b

a

-

-

^

c

b

^

Braids with Reversals and Twists No: 34 – Special As with previous braids, the strands of this braid must be placed in the right place after braiding. It ultimately yields a beautiful eight-strand braid with Reversals.

Table 34

1

2

3

4

e

1 (4L/4R)

^

-

3

4

*

*

e

4

*

*

-

2 (3L/5R) 3 (4L/4R) 4 (3L/5R)

^

-

-

d

c

b

a

d

-

-

^

d

c

-

^

Braids with Reversals and Twists No: 35 - Twins What is special about this braid is that the strands in steps 1 and 3 are not moved to the other hand but keep to the inside of the same hand! With this braid it is rather tricky to keep the strands in the right position during the braiding.

#

+

#

+

Table 35

1

2

3

4

5

1 (4L/3R)

^

2

-

-

*

2 (4L/3R)

^

-

3

4

x

3 (3L/4R) 4 (3L/4R)

*

e

d

o

#

o

c

b

a

* *

-

-

b

^

x

d

c

-

^

Braids with Reversals and Twists No: 36 - Wrought Mat This is a variation of a Wrought Mat. Although you may argue that it is not really a braid, at least the Twists are clearly present. At a Twist two strands twist around each other and both change direction. The braiding is mainly held in your left hand. Start this braid with steps 1 to 4 and then repeat only step 4 to make the braid longer.

Braiding with Twists requires a new technique. Normally there is only one active strand for every braiding step, but after a Twist you continue with a different strand. For example: in step 4, strand 8 starts as active strand, passes over 7, under 6, and then twists right (R) around strand 5. Next, strand 5 continues as active strand under 4 and twists right (R) around strand 3. Then strand 3 continues as active strand under 2, over 1 and finishes completely left.

For the advanced: you can choose to first make a three-strand braid for the left side of the mat and use it to fix the other strands onto it during braiding. Finally, it is good practice to always give the strands a little bit of torsion to prevent the end result from twisting.

Table 36

(0)

1

2

3

4

1 (8L)

*

1

^

2 (8L)

*

1

3 (8L)

*

4 (8L)

*

5

6

-

R

^

1

-

R

-

R

^

1

-

R

-

R

-

7

8

7

^

Braids with Reversals and Twists No: 37 – Three Joined Braids As with the previous Wrought Mat, the Braid Scheme has to explain how to braid. In the Table, L stands for left or counter-clockwise rotation and R for ..., yes, right or clockwise rotation.

x

x

x

o

o

Table 37

1

2

3

4

5

e

1 (5L/4R)

^

2

-

L

-

*

*

-

2 (4L/5R)

o

+

+

+

d

c

b

a

R

-

b

^

Braids with Reversals and Twists No: 38 - Swing To conclude this chapter two braids with Reversals and Twists. Pay attention, at steps 1 and 3 the strand stays in the same hand. It is good practice to give the strands a little bit of torque to prevent the end result from twisting.

Table 38

1

2

3

4

1 (3L/2R)

^

L

3

*

2 (3L/2R)

^

-

3

x

3 (2L/3R) 4 (2L/3R)

*

d

c

b

a

* *

-

L

^

x

-

b

^

Braids with Reversals and Twists No: 39 – Zigzag The last braid with Reversals and Twists.

Table 39

1

2

1 (5L/2R)

3

4

5

^

4

-

2 (4L/3R)

^

L

3

4

x

3 (3L/4R)

^

-

3

x

x

4 (2L/5R) 5 (3L/4R) 6 (4L/3R)

* * *

e

d

c

b

a

* * * -

d

^

x

d

c

R

^

x

x

c

-

^

Two Cell Thick Braids No: 40 - Horizontal Herringbone Braid No: 3 is a braid with a herringbone pattern. In the Braid Scheme this can be found as double vertical rows of crossings where the strands cross in the same direction. By rotating this pattern 90 degree you get a horizontal herringbone pattern. The Diagram of this braid shows how the strands not only intersect in a flat surface, but also follow a braid pattern in depth, the braid gains more thickness. In this chapter, braids of two cells thick are discussed.

+

o

+

o

+

Table 40

1

2

3

4

5

f

1 (5L/5R)

^

-

-

4

5

*

*

f

-

*

*

-

2 (4L/6R) 3 (5L/5R) 4 (4L/6R)

^

2

3

-

o

+

o

+

o

e

d

c

b

a

-

-

c

b

^

e

d

-

-

^

Two Cell Thick Braids No: 41 – Rectangle Here is a full and regular braid. Quite difficult to make but the end result is beautiful.

o

#

o

#

o

#

o

Table 41

1

2

3

4

5

6

7

h

1 (7L/7R)

^

2

3

4

5

-

7

*

*

h

-

*

*

-

2 (6L/8R) 3 (7L/7R) 4 (6L/8R)

^

-

-

-

-

6

#

o

#

o

#

o

#

g

f

e

d

c

b

a

-

f

-

-

-

-

^

g

-

e

d

c

b

^

Two Cell Thick Braids No: 42 – Large Rectangle This is a less tight but much easier to make alternative to the previous braid. The added value of this braid is that by extending the pattern, braids of 20 or even 28 strands are possible. With the 20-strand version you do not braid under/over the 1st two but 1st four strands. With the 28-strand version, you braid under/over the first six strands. The photo shows a version with 20 strands.

o

#

o

#

o

#

Table 42

1

2

3

4

5

6

g

1 (6L/6R)

^

2

3

-

-

-

*

*

g

6

*

*

-

2 (5L/7R) 3 (6L/6R) 4 (5L/7R)

^

-

-

4

5

#

o

#

o

#

o

f

e

d

c

b

a

f

e

d

-

-

^

-

-

-

c

b

^

Two Cell Thick Braids No: 43 – Fish-Method This braid holds the key to the design of Two Cells Thick Braids. In the Braid Scheme you can see columns with a number of diagonal crossings in the same direction (right to left or left to right). These columns are responsible for the various elements of the Diagram. The width of these columns determines which element. For instance; an 1,5-1,5 hourglass requires a column of 4 diagonal crossings (see No: 41). This braid is called Fish because with a little imagination the Diagram resembles a fish.

Designing a braid with the Fish-Method: Step 1: Draw the Diagram of the braid you want to make (It may be helpful to read the chapter “About Cells”).

Step 2: Draw the Braid Scheme: Recognise the various elements of the diagram and transfer these elements to the Braid Scheme as columns of diagonal crossings (each element corresponds with a distinct numbers of diagonal crossings).

Step 3: Draw the braiding steps in the Braid Scheme (orange).

Step 4: Fill the Braiding Table with the information of step 3.

Note: The Fish-Method is limited to braids that are symmetrical front and back, see No: 49 and following.

x

o

x

o

x

o

Table 43

1

2

3

4

5

6

g

1 (6L/6R)

^

-

3

-

5

6

*

*

g

-

*

*

-

2 (5L/7R) 3 (6L/6R) 4 (5L/7R)

^

2

-

4

-

o

x

o

x

o

x

f

e

d

c

b

a

f

-

d

-

-

^

-

e

-

c

b

^

Two Cell Thick Braids No: 44 – Diagonal By combining the columns of diagonals (see No: 43 – Fish-Method) in different ways you can easily design different braids. Here are some examples.

Table 44

1

2

3

4

5

e

1 (5L/4R)

^

2

3

4

5

*

*

e

-

*

*

-

2 (4L/5R) 3 (5L/4R) 4 (4L/5R)

^

-

-

-

d

c

b

a

-

c

-

^

d

-

b

^

Two Cell Thick Braids No: 45 – Hollow Rectangle Another Fish-Method (No: 43) design.

Table 45

1

2

3

4

5

e

1 (5L/4R)

^

-

3

4

5

*

*

e

-

*

*

-

2 (4L/5R) 3 (5L/4R) 4 (4L/5R)

^

2

-

-

d

c

b

a

-

c

b

^

d

-

-

^

Two Cell Thick Braids No: 46 – Dome Another illustration of the Fish-Method.

Table 46

1

2

3

4

5

e

1 (5L/4R)

^

2

3

-

-

*

*

e

5

*

*

-

2 (4L/5R) 3 (5L/4R) 4 (4L/5R)

^

-

-

4

d

c

b

a

-

-

b

^

d

c

-

^

Two Cell Thick Braids No: 47 – Star The possibilities of the Fish-Method (No: 43) are countless. Here an extension of the possibilities with a diagonal of 3 crossings along the edge.

With braid No: 23 it is explained how to make a transition from one braid pattern to another. With designs of the Fish-Method, this can be done relatively easily. For example, this design can be alternated with No: 81 without the need for transition pieces.

o

+

o

+

Table 47

1

2

3

4

e

1 (4L/4R)

^

2

3

4

*

*

e

-

*

*

-

2 (3L/5R) 3 (4L/4R) 4 (3L/5R)

^

-

-

+

o

+

o

d

c

b

a

-

-

-

^

d

c

b

^

Two Cell Thick Braids No: 48 – Trapezoid Asymmetrical designs are also possible, here a fine little trapezoid.

Table 48

1

2

3

4

d

1 (4L/3R)

^

2

3

-

*

*

-

4

*

*

d

2 (3L/4R) 3 (4L/3R) 4 (3L/4R)

^

-

-

c

b

a

c

b

^

-

-

^

Two Cell Thick Braids No: 49 – Belly Braids designed with the Fish-Method are symmetrical front and back. By making creative use of diagonals in the braid scheme, braids with different fronts and backs are also possible.

Table 49

1

2

3

4

5

e

1 (5L/4R)

^

2

3

4

5

*

*

e

-

*

*

-

2 (4L/5R) 3 (5L/4R) 4 (4L/5R)

^

-

-

4

d

c

b

a

-

c

-

^

-

-

b

^

Two Cell Thick Braids No: 50 – Vice Versa This is an extension of the previous braid.

+

o

+

o

+

o

Table 50

1

2

3

4

5

6

g

1 (6L/6R)

^

2

3

-

5

-

*

*

g

6

*

*

-

2 (5L/7R) 3 (6L/6R) 4 (5L/7R)

^

-

-

4

5

o

+

o

+

o

+

f

e

d

c

b

a

f

-

d

-

-

^

-

-

-

c

b

^

Two Cell Thick Braids No: 51 – Hourglass In my opinion, the middle pairs of cells in a two cell thick braid look somewhat like an hourglass. The middle hourglass in this design is skewed.

Table 51

1

2

3

4

5

e

1 (5L/4R)

^

2

3

4

5

*

*

e

-

*

*

-

2 (4L/5R) 3 (5L/4R) 4 (4L/5R)

^

-

-

4

d

c

b

a

d

c

-

^

d

-

b

^

Two Cell Thick Braids No: 52 – Contorsion The final braid of this chapter is a combination of the two previous ones. In this braid the strands push each other in all sorts of bends and the braid therefore has a very open character. It is possible to widen this braid by adding a skewed 1.5-1.5 hourglass in the middle. This will be even more slanted than the one in braid No: 51.

o

+

o

+

o

Table 52

1

2

3

4

5

f

1 (5L/5R)

^

2

-

-

5

*

*

f

5

*

*

-

2 (4L/6R) 3 (5L/5R) 4 (4L/6R)

^

-

3

-

+

o

+

o

+

e

d

c

b

a

-

d

c

-

^

-

d

-

b

^

About Cells No: 53 - Cells in a Diagram When you want to design braids yourself, it is worth taking a closer look at the Diagram.

The Diagram is the cross section of a braid It shows the lines or tracks along which the strands move. A Diagram is build up of closed figures wich are called cells. In these cells the strands rotate in the same direction along the circumference. There is usually a number in such a cell, this indicates how many strands are occupied by this cell in the braid. This is further explained in the following drawings:

Drawing A) This is not a braid yet. Here, three strands are twisted together as in a rope to form a bundle.

Drawing B) This is the Diagram of a flat 5-strand braid. Two basic cells of 3 come together. You can imagine this as 2 oppositely rotating parallel ropes where the strands cross at the point of contact from one rope to the other and vice versa. Interlocking cells always run in opposite directions. When designing flat braids, it is useful to assume that every time a cell comes in contact with a neighbouring cell, it needs half a strand less. In this case the two base cells of 3 both become cells of 2.5. A 2.5-strand cell appears strange at first sight. It may help to realize that there are also empty positions between the strands where strands can cross.

A 2.5 cell then has a total of 5 positions (2 * 2.5) on the circumference of which alternately 2 and 3 positions are occupies by a strand: on average 2.5.

Drawing C) Furthermore, embroidering on the principles explained at B), two flat 5-strand braids deliver an 8-strand circular braid. The individual strands are no longer drawn in this Diagram.

Drawings D) and E) are a further continuation of the principle.

About Cells No: 54 - The Outer Look of a Braid The cells on the outside of the braid are recognizable. This is shown in the following drawings. The pluses in the bottom two drawings indicate where the strands go deeper into the braid. These drawings can be helpful to figure out the Diagram of a new braid.

Diagram-Method No: 55 - The Principle I developed the Diagram-Method to translate a Diagram into a Braid Scheme. Although there are limitations, the method delivers useful results. It also provides a great deal of insight into the structure of braids.

The principle of the method is as follows: A Diagram pictures the cross section of a braid. The lines indicate the track(s) along which the strands of the braid move. The positions of the strands are now drawn on these lines at successive positions in the braid. These positions correspond to rows of crossings in the Braid Scheme. It is then possible for each crossing of strands in the Braid Scheme to find the two corresponding strands in the Diagram. You can there see which strand crosses in front of the other and whether it crosses from right to left or from left to right. This sounds pretty complicated, I worked this out with an example of a 5-strand flat braid.

Step 1) The process starts with a number of vertical lines (black dotted lines). The distance between two lines (aka 1 unit) corresponds to 1 strand. So for this 5strand braid, 6 vertical lines are required.

Step 2) Draw the diagram at the top. Note that the outer cells of 1.5 strands are 1.5 units wide and the middle cell of 2 strands is 2 units wide.

Step 3) Determine the number of horizontal rows of crossings of the Braid Scheme. This number is equal to the number of tracks that crosses each vertical line (except at the two reversals at the outer edges): in this case two. Give these rows the letters “a” and “b”, this is shown in orange. A further clarification of this step: the braid pattern is repeated after two rows of crossings.

Step 4) Starting on the left side of the Diagram, follow the track and name the positions where the track crosses a vertical line “a”, “b”, “a”, “b”, etc. Keep going until you are back at the starting position. The direction of rotation does not matter in this case (*). Indicate the direction of movement of each point with a small arrow.

Step 5) Then continue by drawing in the Braid Scheme the crossings. Start on the left on row “a” with a reversal. The next crossing on row “a” is on the vertical line immediately below the two “a”’s in the Diagram. The lower “a” in the diagram (the one at the front of the braid) determines the direction of the crossing in the Braid Scheme. This point moves to the left. This means that on row “a” in the Braid Scheme you draw a dash from the top right to the bottom left. You do the same for all crossings on rows “a” and “b”. (*) With Diagrams with multiple tracks it different tracks and what direction of look at comparable designs with only Diagram (=1 track) instead of 2 by 2

is less obvious with which letter to start on the rotation to choose. Sometimes it can be helpful to 1 track. For example, look at a 2 by 3 cell cell Diagram (2 tracks).

Diagram-Method No: 56 – Comments The Diagram Method needs some attention. An important one comes from the fact that the number of strands of a cell is only determined by the width (and not by the height). As an explanatory example here the same Diagram of the 5-strand flat braid, but now vertically instead of horizontally.

For various reasons, it is desirable (but not necessary) that all reversals of tracks are on the outside of the Diagram. All three cells are therefore equally wide in this case. The three cells are spread over 5 units and each cell therefore basically contain 1 2/3 strand. It is now case to just continue to draw the Braid Scheme and to test the result experimentally.

In this case the Diagram-Method produces the same flat braid as in the horizontal diagram with 1.5-2-1.5 cells. Apparently there is only limited control over the distribution of the strands across the cells. With a different number of strands these are the results: 4 5 6 7

strands strands strands strands

delivers 1.5-1-1.5 delivers 1.5-2-1.5 is not possible delivers 2.5-2-2.5

Diagram-Method No: 57 Variables of Flat Braids In the previous example (No: 56) it proved impossible to design a braid with 6 strands.

This brings us to the next point of attention of the method. For a given Diagram not every arbitrary number of strands can be chosen. This is not a limitation of the Diagram-Method but a characteristic of flat braiding. All the braids in this book are flat braids: they are, as is clear from the Braid Schemes, braided in a two-dimensional plane.

The possible number of strands for a given Diagram is determined by the number of horizontal rows of crossings in the Braid Scheme (see No: 55, step 3) and the number of Tracks in the Diagram. See for example, braid No: 58: this Braid Scheme has six horizontal rows of crossings and 9 strands move across 3 tracks.

For the first example in this chapter (No: 55, one track, two rows of crossings), there are no restrictions on the number of strands. With the second example (No: 56, one track, six rows of crossings) the number of strands cannot be a multiple of three: 6 strands are not possible. These properties follow from the following two facts. 1) The length of each track (in units) is a multiple of the number of rows of crossings. 2) The reversals along the edge cannot have the same letters. For example, this leads for Diagrams with one track to the conditions mentioned in the following drawings.

"S" stands for the number of strands "R" for the number of horizontal rows of crossings "N" stands for a Natural (whole) number

Diagram-Method I do not work out all situations separately but give a summary:

Summary of the number of strands of different Diagrams 2 rows, always 1 track 4 rows, 1 track 2 tracks 6 rows, 1 track 3 tracks 8 rows, 1 track 2 tracks 4 tracks

=> => => => => => => =>

any number of strands possible number of strands no multiple of two number of strands multiple of two number of strands no multiple of three number of strands multiple of three number of strands no multiple of two number of strands multiple of two number of strands multiple of four

When you use the Diagram-Method, the number of strands has to satisfy these requirements.

Diagram-Method No: 58 – Three by Three Square It might be enlightening to look at an example. This is the Nine Strand Square (No: 72) from the chapter "Three or More Cells Thick Braids". This example has six horizontal rows of crossings. The braid pattern is repeated after six horizontal rows of crossings, six braid steps are needed. Furthermore, three separate tracks can be distinguished in the Diagram.

The Braid Scheme may make it clear that this is only possible if the number of strands is a multiple of three.

Diagram-Method No: 59 – Simple Blok Braid As an example of the Diagram-Method here a rectangle with 4 rows and 2 tracks. The requirement is therefore that the number of strands must be a multiple of two. In this case 10 strands are chosen. This is a variation of rectangular braid No: 41.

x

o

x

o

x

Table 59

1

2

3

4

5

f

1 (5L/5R)

^

2

3

-

5

*

*

f

-

*

*

-

2 (4L/6R) 3 (5L/5R) 4 (4L/6R)

^

-

-

4

o

x

o

x

o

e

d

c

b

a

-

d

-

-

^

e

-

c

b

^

Reversed-Diagram-Method No: 60 - The Principle A Braid Scheme can be translated into a Diagram, since it contains all necessary information. The tricky part is that the crossings in the Braid Scheme only provide information about the position of crossing strands relative to each other at the point of crossing but no information about the position in the finished braid. I use the following method that provides useful results for simpler braids.

Step I) Draw the Braid Scheme, as an example I use a horizontal herringbone (No: 40).

Step II) Draw two points under each column of crossings. I simplify the situation by assuming that at each crossing of two strands one strand is at the front and one strand is at the back of the braid. The top row of points are the back, the bottom row of points are the front of the braid.

Step III) Indicate at each point with a letter which horizontal row of crossings it concerns.

Step IV) Starting with the bottom (front) row, indicate with an “<” or “>” next to each letters the direction of that strand. The direction follows directly from the direction of the crossings in the Braid Scheme. For the sake of clarity, this is done with red and blue in the drawing. Then assign the opposite direction to the letters of the top (back) row.

Step V) Draw the tracks of the Diagram by following the positions of the strands. Start at the reversal “a” on the left side and continue with b, c, d, a, etc. While you do this follow the directions of the arrows. The second letter b with the correct direction is on the bottom (front) and so is c. However, the letter d is again at the top (back). Draw the complete tracks in this way. Note: the preceding and the following positions of a strand determine the position of a track at the reversal (on the edge of the braid). This can be on the front or back, but also in the middle!

Reversed-Diagram-Method

No: 61 - A Refinement

The method provided a good Diagram for the previous braid. The situation becomes different with braids with larger cells or multiple layers. The following method is then necessary to prevent the Diagram from becoming cluttered by tracks zigzagging from front to back, or even showing non-existent crossings.

I) For consecutive series of two or more points on the same side of the braid (front or back), connect the outer two points together with an arc. Orange bows in the drawing.

II) Ignore floating points. Floating points are points of which the preceding and the following point lie on the other side of the braid. Black letters in the drawing.

III) Connect each series (see I), with a straight line to the subsequent series. Ignore the loose points (see II). Green lines in the drawing.

NB: The outside sides seem to deviate somewhat from these instructions but also follow these rules.

This method produces a useful diagram for common braids, with exotic patterns sometimes not. When in doubt always compare the Diagram with a physical braid.

Alternative-Diagram-Method The Reversed-Diagram-Method seems to offer another interesting possibility. By using the method in reverse, it should also be possible to translate a Diagram into a Braid Scheme (as is done with the Diagram-Method) For this it is necessary to have more insights into the rules that apply to the Diagrams (these rules are an addition to those of the DiagramMethod described earlier). An obvious rule is, for example, that the crossing from front to back always involves an odd number of units. Another observation is that the width of an arc plus any adjacent free space is determined by the underlying cell (s). To further elaborate on this, it is necessary to analyse multiple Diagrams made with the ReverseDiagram-Method. This book supplies sufficient material for this, preferably choose as different braids as possible.

Designing a Block Braid No: 62 â&#x20AC;&#x201C; The Fast Method To design a block braid it is not always necessary to work out the complete braid via the Diagram-Method. As an example this is the design of a rectangular braid of 3 by 4 cells and 11 strands as shown in the diagram below. You can look at this braid like four adjoining vertical 1.5-2-1.5 braids.

For the explanation of the Diagram-Method I designed a vertical 1.5-2-1.5 braid. When you take a closer look at that diagram (No: 63), you can spot the two required sub-elements for the block braid. Important in this step is to carefully consider the number of strands that make up the sub-element, this equals the number of units it is wide.

Now that the sub-elements are known, they can be combined (see Braid Scheme above): - Draw a grid of 12 vertical (= 11 units for 11 strands) and six horizontal lines.

- Draw the centreline of the braid in the middle.

- Draw a middle sub-element (0.5-1-0.5) left of this centreline - Then draw the second middle sub-element right of this centreline. Important: the directions of the crossings of this second sub-element have to fit to fit to those of the first sub-element. This is not always a straightforward process; it now comes down to a perhaps aesthetic view. The rule seems to be that with an even number of strands (as in this case, two), the direction of all the crossings change. In the case of a subelement with an odd number of strands, the direction remains the same, but the pattern is mirrored exactly on the boundary line (see first braid of No: 66).

- Finally, also fit the outer sub-element (1-1.5-1) on both sides.

Designing a Block Braid No: 63 - Vertical 1,5-2-1,5 Braid This is the vertical 1.5-2-1.5 braid containing the two sub-elements of the previous block braid.

Designing a Block Braid No: 64 - Examples These are a other designs to illustrate the method.

Designing a Block Braid No: 66 - Examples (continued) Here are two final designs to illustrate this method.

Three or More Cells Thick Braids No: 67 â&#x20AC;&#x201C; Braid with Triple Edge In this chapter, braids of more than two cells thick are discussed. This braid pattern is a continuation of the 2-cell thick braid with herringbone pattern (No: 40). With three rows of rectangular crossings, the braid becomes three cells thick. The middle cells have the value zero. This seems peculiar but means that the strands of the adjacent cells connect to each other in the same horizontal plane or that they cross the cells with the value zero. The diagram is drawn as a rectangle to indicate all lanes and cells properly. In practice, the braid will have some thickness along the edge but will be flatter especially in the middle (see braid No: 111 for more information about this phenomenon).

#

+

o

#

+

Table 67

1

2

3

4

5

e

1 (5L/4R)

^

2

3

4

-

*

*

e

-

*

*

-

5

*

*

-

2 (4L/5R) 3 (5L/4R)

^

2

-

-

4 (4L/5R) 5 (5L/4R) 6 (4L/5R)

^

-

-

4

o

+

#

o

d

c

b

a

d

-

-

^

d

c

b

^

-

-

b

^

Three or More Cells Thick Braids No: 68 â&#x20AC;&#x201C; Braid with Quadruple Edge The obvious continuation of the previous braid has a quadruple edge.

o

+

x

#

Table 68

1

2

3

4

e

1 (4L/4R)

^

2

3

4

*

*

e

-

*

*

e

-

*

*

-

4

*

*

-

2 (3L/5R) 3 (4L/4R)

^

2

-

4 (3L/5R) 5 (4L/4R)

^

-

-

6 (3L/5R) 7 (4L/4R) 8 (3L/5R)

^

-

3

#

x

+

o

d

c

b

a

-

-

-

^

d

c

-

^

d

c

b

^

-

-

b

^

Three or More Cells Thick Braids No: 69 â&#x20AC;&#x201C; Nine Strand Rectangle A block braid with more body than the previous one.

x

+

o

x

+

Table 69

1

2

3

4

5

e

1 (5L/4R)

^

2

3

-

-

*

*

-

5

*

*

e

5

*

*

-

2 (4L/5R) 3 (5L/4R)

^

-

-

-

4 (4L/5R) 5 (5L/4R) 6 (4L/5R)

^

-

3

4

o

+

x

o

d

c

b

a

-

-

b

^

d

-

-

^

d

c

b

^

Three or More Cells Thick Braids No: 70 â&#x20AC;&#x201C; Crown A design with six floating cells.

Table 70

1

2

3

4

5

6

7

g

1 (7L/6R)

^

2

3

4

5

6

-

*

*

-

7

*

*

-

-

*

*

g

2 (6L/7R) 3 (7L/6R)

^

2

-

-

5

-

4 (6L/7R) 5 (7L/6R) 6 (6L/7R)

^

-

-

4

-

-

f

e

d

c

b

a

-

-

d

-

-

^

f

e

d

c

b

^

-

e

-

-

b

^

Three or More Cells Thick Braids No: 71 â&#x20AC;&#x201C; Pinned Unexpected designs are possible with the Diagram-Method. This is a 6-strands round braid, crossed by a 3-strands flat braid.

+

#

o

+

#

Table 71

1

2

3

4

5

e

1 (5L/4R)

^

-

3

-

5

*

*

e

5

*

*

e

-

*

*

-

2 (4L/5R) 3 (5L/4R)

^

2

3

4

4 (4L/5R) 5 (5L/4R) 6 (4L/5R)

^

-

-

-

o

#

+

o

d

c

b

a

-

c

b

^

d

-

-

^

-

c

-

^

Three or More Cells Thick Braids No: 72 â&#x20AC;&#x201C; Nine Strand Square Due to a small adjustment, the design of a rectangular block braid produced a pointsymmetrical square braid. Sometimes different paths lead to the same result: this braid returns as No: 77 in the chapter " Multiple Cells Round Braids". This braid needs a 3-strand twisted core (see No: 30).

+

o

x

+

o

Table 72

1

2

3

4

5

e

1 (5L/4R)

^

-

3

-

-

*

*

e

5

*

*

e

-

*

*

-

2 (4L/5R) 3 (5L/4R)

^

2

3

4

4 (4L/5R) 5 (5L/4R) 6 (4L/5R)

^

-

3

4

x

o

+

x

d

c

b

a

-

-

b

^

d

-

b

^

-

-

-

^

Three or More Cells Thick Braids No: 73 â&#x20AC;&#x201C; Twelve Strand Square This is a second point symmetrical square.

o

x

+

o

x

+

Table 73

1

2

3

4

5

6

g

1 (6L/6R)

^

2

3

4

5

-

*

*

-

6

*

*

-

-

*

*

g

2 (5L/7R) 3 (6L/6R)

^

-

-

4

-

4 (5L/7R) 5 (6L/6R) 6 (5L/7R)

^

-

3

-

-

+

x

o

+

x

o

f

e

d

c

b

a

f

-

-

-

-

^

-

e

-

c

b

^

f

e

d

-

b

^

Three or More Cells Thick Braids No: 74 â&#x20AC;&#x201C; Fifteen Strand Square Here a point symmetrical square with a lot of strands.

I sometimes use a tool when braiding with a lot of strands. I clamp a board onto the table edge in front of me. I clamp three slats as spacers underneath so there are two gaps between the tabletop and board, one on the left and one on the right. Through these gaps the strands of the left and right bundle can lie next to each other but there is not enough space to cross over each other. In this way the bundles remain under the board in the right order. I only remove the active strand from it to braid and then put it back under the board in the right place. Another option is an exercise in cooperation: to braid with two people, one person taking care of the left bundle and the other the right bundle.

Table 74

o 1

x 2

+ 3

o 4

x 5

+ 6

o 7

x 8

h

1 (8L/7R)

^

2

3

-

5

6

-

-

*

*

-

8

*

*

h

8

*

*

-

2 (7L/8R) 3 (8L/7R)

^

-

-

-

-

-

-

4 (7L/8R) 5 (8L/7R) 6 (7L/8R)

^

-

3

4

-

6

7

+ g

x f

o e

+ d

x c

o b

+ a

-

-

e

-

-

b

^

g

-

-

d

-

-

^

g

f

e

d

c

b

^

Multiple Cells Round Braids No: 75 â&#x20AC;&#x201C; Radial Herringbone When you design round braids with braid patterns of multiple cells thick, this can lead to surprising diagrams. This chapter contains some examples. This braid is the result of a round braided herringbone (No: 40).

The method of No: 9 is used for this and the following braid; by weaving twice from the same hand, the actions on the left and right are symmetrical.

o

#

o

#

x

+

x

+

Table 75

1

2

3

4

d

c

b

a

1 (4L/4R)

^

-

c

b

-

on (5)

2 (4L/4R)

^

-

-

b

a

on (5)

3 (4L/4R)

-

2

3

-

^

on (e)

4 (4L/4R)

1

2

-

-

^

on (e)

Multiple Cells Round Braids No: 76 â&#x20AC;&#x201C; Hula Hoop Here a continuation of the previous braid with larger hourglasses (No: 41).

o

#

o

#

o

#

x

+

x

+

x

+

Table 76

1

2

3

4

5

6

f

e

d

c

b

a

1 (6L/6R)

^

-

-

-

-

b

-

on (7)

2 (6L/6R)

^

f

e

d

-

b

-

on (7)

3 (6L/6R)

-

2

-

-

-

-

^

on (g)

4 (6L/6R)

-

2

-

4

5

6

^

on (g)

Multiple Cells Round Braids No: 77 â&#x20AC;&#x201C; Eleven Strand Square The Braid Schemes of this and the following braids looks complicated but almost automatically follow from the drawings of the outside of braids from the chapter "About Cells" (No: 54). The same braid was braided as a flat braid in the "Three or More Cells Thick Braids" chapter (No: 72).

o

+

o

+

o

+

x

x

x

Table 77

1

2

3

4

5

6

c

b

a

1 (6L/3R)

-

2

3

-

5

6

2 (6L/3R)

^

c

3 (6L/3R)

^

-

^

on (7)

-

-

on (d)

b

-

on (d)

Multiple Cells Round Braids No: 78 â&#x20AC;&#x201C; Eleven Strand Triangle This braid, like previous braid, follows from the drawings of the outside of braids from the chapter "About Cells" (No: 54). Because of the way the braids of this chapter are made, they are often rather "full" on the inside and "open" on the outside. Be careful when working up after braiding because it is difficult to maintain the regularity of the braids.

Table 78

1

2

3

4

5

6

7

d

c

1 (7L/4R)

1

2

3

4

-

6

7

2 (7L/4R)

^

-

c

3 (7L/4R)

^

-

-

b

a ^

on (8)

-

-

on (e)

-

a

on (e)

Multiple Cells Round Braids No: 79 â&#x20AC;&#x201C; Sixteen Strand Square This graceful braid can only be braided with aids or with two people (see No: 74). Consider also after how many horizontal rows of crossings a pattern repeats. This pattern repeats itself after eight vertical rows and can therefore be braided with 8, 16, 24, ... strands (although perhaps not every number provides a stable braid). With eight strands, this pattern provides a charming zigzag braid. In that case, drop strand 1, 2, 3, 4, a, b, c and d. With all the braids of this chapter it is an entertaining exercise to figure out what the Diagram will look like with another number of strands.

o

+

o

+

o

+

o

+

x

#

x

#

x

#

x

#

Table 79

1

2

3

4

5

6

7

8

h

g

f

e

d

c

b

a

1 (8L/8R)

-

-

-

-

-

6

7

8

2 (8L/8R)

^

3 (8L/8R)

1

4 (8L/8R)

^

^ on (i) h

2

-

4

5

-

7

-

f

-

d

c

-

-

a on (9) ^ on (i)

-

g

f

e

-

-

-

- on (9)

Linked Braids No: 80 â&#x20AC;&#x201C; Double Flat Braid It is possible to immediately draw the Braid Scheme of reasonably complex braids.

Although these Schemes look complicated, the principle is simple. The idea is to braid two or three flat braids on top of each other and connect them or cross them at different points. To clarify this: here is the Braid Scheme of two braids above each other (without connections or crossings).

o

+

o

+

Table 80

1

2

3

4

e

1 (4L/4R)

^

2

3

4

*

*

e

-

*

*

e

2 (3L/5R) 3 (4L/4R) 4 (3L/5R)

^

-

3

+

o

+

o

d

c

b

a

d

-

b

^

-

-

-

^

Linked Braids No: 81 â&#x20AC;&#x201C; Linked Round Braid with Herringbone Pattern With this braid, the two braids lying one above the other are connected to each other along the outer edges, creating a round braid. For this particular braid this way of braiding is considerably easier than according the traditional way (No: 10).

When you feel like puzzling, it is a fun exercise to figure out how the two seemingly different patterns of No:10 and No:81 yield the same braid. Notice further that the FishMethod (No: 43) produces the same Braid Scheme.

o

+

o

+

Table 81

1

2

3

4

e

1 (4L/4R)

^

2

3

4

*

*

-

-

*

*

e

2 (3L/5R) 3 (4L/4R) 4 (3L/5R)

^

-

-

+

o

+

o

d

c

b

a

-

-

-

^

d

c

b

^

Linked Braids No: 82 â&#x20AC;&#x201C; Linked Braid I This braid consists of two superimposed 5-strand flat braids that are coupled along the edges.

o

+

o

+

o

Table 82

1

2

3

4

5

f

1 (5L/5R)

^

2

3

4

-

*

*

-

-

*

*

f

2 (4L/6R) 3 (5L/5R) 4 (4L/6R)

^

2

3

-

+

o

+

o

+

e

d

c

b

a

-

-

c

b

^

-

d

c

b

^

Linked Braids No: 83 â&#x20AC;&#x201C; Linked Braid II As before, this braid consists of two superimposed 5-strand flat braids that are connected to each other on the edges. The link is just slightly different.

Linked braids often become rather loose. The following method leads to more firm braids.

Hold the strands of the left and right hand at an angle of 90 degrees to each other when braiding. After each step, pull the left and right hands apart (without disturbing the order of the strands!) to bring the new made crossings close up to the already finished braid.

Once the braid is finished, it may still be necessary to work it up. Begin at the start or top of the braid and pull each strand a little tighter towards the end of the braid. Do not do this in one go but in a number of steps from start to finish. To neatly work up a braid but still keep it flexible, you can put a temporary core in the braid, for example a metal rod, and remove it after working up the braiding. Another way to get a better shape and distribute the tension of the strands evenly is to occasionally roll the braid between your hands, over your leg or with a coarse braid: under your foot.

+

o

+

o

+

Table 83

1

2

3

4

5

f

1 (5L/5R)

^

-

-

4

5

*

*

-

-

*

*

f

2 (4L/6R) 3 (5L/5R) 4 (4L/6R)

^

2

3

-

o

+

o

+

o

e

d

c

b

a

-

-

c

b

^

e

d

-

-

^

Linked Braids No: 84 â&#x20AC;&#x201C; Number Eight With this braid, the outer sides of the top and bottom braids are connected and the two braids also intersect in the middle. The cross-section thus forms an "eight". However, more roads lead to Rome: this and some more braids from this chapter can be designed faster using the Fish-Method (No: 43).

+

o

+

o

+

Table 84

1

2

3

4

5

f

1 (5L/5R)

^

2

3

-

5

*

*

-

-

*

*

f

2 (4L/6R) 3 (5L/5R) 4 (4L/6R)

^

-

-

4

o

+

o

+

o

e

d

c

b

a

-

d

-

-

^

e

-

c

b

^

Linked Braids No: 85 â&#x20AC;&#x201C; Pull Something strange happens when braiding this braid. In step 1 you have to pull strand 1 under strand 2 (pull hard enough). In step 2, something similar happens at the bottom.

Another thing is that in the middle of this braid the strands run as pairs. See also Duo (No: 107) braid in the "Bonus" chapter.

+

o

+

o

+

Table 85

1

2

3

4

5

f

1 (5L/5R)

^

-

3

5

5

*

*

f

-

*

*

f

2 (4L/6R) 3 (5L/5R) 4 (4L/6R)

^

-

-

4

o

+

o

+

o

e

d

c

b

a

-

-

-

b

^

e

-

c

b

^

Linked Braids No: 86 â&#x20AC;&#x201C; Linked Braid with Reversals In principle it is possible to link all kinds of patterns together. This is a braid with reversals.

Table 86

+

+

o

o

+

+

1

2

3

4

5

6

g

^

3

4

5

6

*

*

-

6

*

*

-

-

*

*

g

-

*

*

g

1 (6L/6R) 2 (5L/7R) 3 (6L/6R)

^

-

3

4

5

4 (5L/7R) 5 (6L/6R)

^

-

-

-

6 (5L/7R) 7 (6L/6R) 8 (5L/7R)

^

2

-

-

-

o

o

+

+

o

o

f

e

d

c

b

a

-

-

-

-

^

-

-

-

-

b

f

e

d

c

^

f

e

d

c

-

^

^

Linked Braids No: 87 â&#x20AC;&#x201C; Linked Braid with Twists I The name needs no further explanation.

Table 87

+

+

o

o

1

2

3

4

e

^

3

4

*

*

-

-

*

*

-

-

*

*

e

4

*

*

e

1 (4L/4R) 2 (3L/5R) 3 (4L/4R)

^

-

3

4 (3L/5R) 5 (4L/4R)

^

-

6 (3L/5R) 7 (4L/4R) 8 (3L/5R)

^

2

-

o

o

+

+

d

c

b

a

d

c

^

d

c

-

-

-

^

-

-

b

^

^

Linked Braids No: 88 â&#x20AC;&#x201C; Linked Braid with Twists II Many Braid Schemes in this chapter seem quite unclear. Although I designed them myself at the time, I now sometimes find it difficult to tie a rope to it (a Dutch expression). This design takes advantage of the fact that it is relatively easy to connect the upper and lower braids with twists. Note that also with this braid the active strand is not always the outer strand.

+

+

#

Table 88

1

2

3

d

1 (3L/3R)

^

-

3

*

*

-

-

*

*

d

3

*

*

-

3

*

8 (2L/4R)

*

-

9 (3L/3R)

^

*

10 (2L/4R)

*

d

11 (3L/3R)

^

*

12 (2L/4R)

*

-

2 (2L/4R) 3 (3L/3R)

^

2

4 (2L/4R) 5 (3L/3R)

^

-

6 (2L/4R) 7 (3L/3R)

^

-

o

o

#

c

b

a

-

b

^

-

b

^

c

-

^

-

b

^

^ ^

Linked Braids No: 89 â&#x20AC;&#x201C; Linked Braid with Reversals and Twists This is a design in line with the previous one but it also contains Reversals. This braid needs a core: after braiding, thread the braid with a core of three strands.

Table 89

+

+

#

#

o

1

2

3

4

5

f

^

-

-

*

*

f

-

*

*

-

-

*

*

f

-

*

*

-

-

*

*

f

-

*

*

-

1 (5L/5R) 2 (4L/6R) 3 (5L/5R)

^

4

4 (4L/6R) 5 (5L/5R)

^

2

-

-

6 (4L/6R) 7 (5L/5R)

^

2

-

4

8 (4L/6R) 9 (5L/5R)

^

-

-

10 (4L/6R) 11 (5L/5R) 12 (4L/6R)

^

2

-

4

o

o

+

+

o

e

d

c

b

a

-

d

-

b

^

-

-

-

^

-

d

-

b

^

-

-

^

-

d

^

-

-

-

b

^

Linked Braids No: 90 â&#x20AC;&#x201C; Six Strand Round Braid I mainly included the next braid for science. The connections on the outside are slightly different from the other braids.

Table 90

1

2

3

d

1 (3L/3R)

^

2

-

*

*

-

-

*

*

d

2 (2L/4R) 3 (3L/3R) 4 (2L/4R)

^

c

b

-

^

-

b

a

^

Linked Braids No: 91 â&#x20AC;&#x201C; Lucky Clover The next braid takes its name from the shape of its cross section. The braid is made up of two flat braids of four strands that cross in the middle.

+

o

+

Table 91

1

2

3

4

e

1 (4L/4R)

^

2

3

4

*

*

e

-

*

*

e

2 (3L/5R) 3 (4L/4R) 4 (3L/5R)

^

-

3

o

+

o

+

d

c

b

a

-

-

-

^

d

-

b

^

Linked Braids No: 92 â&#x20AC;&#x201C; Grand Clover This is a fuller version of the previous braid.

+

o

+

o

+

o

Table 92

1

2

3

4

5

6

g

1 (6L/6R)

^

2

3

4

5

6

*

*

g

-

*

*

g

2 (5L/7R) 3 (6L/6R) 4 (5L/7R)

^

-

3

-

5

o

+

o

+

o

+

f

e

d

c

b

a

-

-

-

-

-

^

h

-

d

-

b

^

Linked Braids No: 93 – Octogram These are two intersecting braids with a horizontal herringbone. The braid is especially pretty if you give the four tracks a different color. I discovered later that the braid becomes better if you go over strand “e” in step 4 and under strand “e” in step 8.

+

o

+

o

Table 93

1

2

3

4

e

1 (4L/4R)

^

2

-

4

*

*

e

-

*

*

-

4

*

*

-

-

*

*

e

2 (3L/5R) 3 (4L/4R)

^

-

-

4 (3L/5R) 5 (4L/4R)

^

2

3

6 (3L/5R) 7 (4L/4R) 8 (3L/5R)

^

-

3

o

+

o

+

d

c

b

a

-

c

-

^

d

c

b

^

-

-

-

^

d

-

b

^

Linked Braids No: 94 â&#x20AC;&#x201C; Moon The floating cells on the edges of this braid tend to turn to one side. The result is a handsome semi-circular braid.

Table 94

+

o

+

o

+

1

2

3

4

5

f

^

-

4

5

*

*

-

5

*

*

f

1 (5L/5R) 2 (4L/6R) 3 (5L/5R) 4 (4L/6R)

^

2

-

-

+

o

+

o

o

e

d

c

b

a

e

-

-

b

^

e

d

-

^

Linked Braids No: 95 â&#x20AC;&#x201C; Star What follows is hardly a braid. There is only 1 layer of strands that all turn in the same direction. A core is necessary to give the braid a stable shape. Be careful not to use strand "a" but strand "b" in step 4!

Table 95

1

2

3

4

c

1 (4L/2R)

^

2

3

4

*

*

c

-

*

*

c

2 (3L/3R) 3 (4L/2R) 4 (3L/3R)

^

-

3

b

a

-

^

^

Linked Braids No: 96 â&#x20AC;&#x201C; Triad Three intersecting braids of three strands form this appealing triangular braid.

+

+

o

#

+

Table 96

1

2

3

4

5

e

1 (5L/4R)

^

-

-

4

5

*

*

-

5

*

*

e

5

*

*

-

2 (4L/5R) 3 (5L/4R)

^

3

4

4 (4L/5R) 5 (5L/4R) 6 (4L/5R)

^

-

-

#

o

#

o

d

c

b

a

-

c

-

^

d

c

b

^

d

^

Braids with Edge Effect No: 97 â&#x20AC;&#x201C; Split When creating new designs, strange things sometimes happen along the edge of a braid.

See No: 33, 34, 85 and also 94. With certain combinations of crossings, some strands do not remain along the edge but shift towards the center of the braid. Some of these combinations are investigated in this chapter.

Table 97

1

2

3

4

5

e

1 (5L/4R)

^

-

3

-

-

*

*

-

-

*

*

-

2 (4L/5R) 3 (5L/4R) 4 (4L/5R)

^

2

-

-

d

c

b

a

-

c

-

^

-

-

b

^

Braids with Edge Effect No: 98 – Rope This pattern is based on the same edge as the previous braid but delivers a different Braid Scheme. The diagrams in this chapter deviate from others in this book. The rules that apply elsewhere are here no longer valid. In the first three braids of the chapter, Tracks split into two Tracks to meet again at another point. Variations are easily made by the way, for example, in steps 2 and 4 cross the active strand over strand “e” instead of under or switch steps 2 and 4 completely.

+

o

+

o

Table 98

1

2

3

4

e

1 (4L/4R)

^

-

-

4

*

*

-

4

*

*

-

2 (3L/5R) 3 (4L/4R) 4 (3L/5R)

^

2

3

o

+

o

+

d

c

b

a

-

c

-

^

-

-

b

^

Braids with Edge Effect No: 99 â&#x20AC;&#x201C; Chain Here two braids with again another edge. This braid requires some extra attention during the braiding to position the strands in the right place. At steps 1 and 4, pull the active strand a little more and at 2 and 3 pull a little less.

Table 99

1

2

3

4

d

1 (4L/3R)

^

2

3

4

*

*

d

4

*

*

d

2 (3L/4R) 3 (4L/3R) 4 (3L/4R)

^

-

3

c

b

a

c

-

^

c

b

^

Braids with Edge Effect No: 100 â&#x20AC;&#x201C; Eye The names of many braids in this book may seem rather farfetched but I believe I really recognize an eye in this braid.

Table 100

1

2

3

4

d

1 (4L/3R)

^

2

3

-

*

*

d

-

*

*

d

2 (3L/4R) 3 (4L/3R) 4 (3L/4R)

^

-

3

c

b

a

-

b

^

-

-

^

Braids with Edge Effect No: 101 â&#x20AC;&#x201C; Ribbon Attractive of Braids with Edge Effect is that small adjustments to the braiding pattern have considerable and often unexpected consequences. The difference with the previous braid is that a small piece of horizontal herringbone is included in the middle. This braid also requires special attention during braiding to get the strands in place. After braiding steps 2 and 3, pull the then outer strand (b and 2) briefly upwards so that it passes under the active strand.

+

o

+

o

Table 101

1

2

3

4

e

1 (4L/4R)

^

-

-

4

*

*

-

-

*

*

e

2 (3L/5R) 3 (4L/4R) 4 (3L/5R)

^

2

-

o

+

o

+

d

c

b

a

-

-

b

^

d

-

-

^

Braids with Edge Effect No: 102 â&#x20AC;&#x201C; MĂśbius This braid is a variation on the previous one, the strands move in pairs but only in one track. With this kind of unusual braiding it is enlightening to draw the diagram via the Reversed-Diagram-Method.

Table 102

1

2

3

4

d

1 (4L/3R)

^

-

3

4

*

*

d

-

*

*

-

2 (3L/4R) 3 (4L/3R) 4 (3L/4R)

^

2

3

c

b

a

c

-

^

c

b

^

Braids with Edge Effect No: 103 â&#x20AC;&#x201C; Epitome Here are three braids with another edge. It took a while to comprehend but a number of elements come together in this fascinating braid of only seven strands.

Table 103

1

2

3

4

d

1 (4L/3R)

^

2

3

-

*

*

-

-

*

*

-

2 (3L/4R) 3 (4L/3R) 4 (3L/4R)

^

2

-

c

b

a

c

b

^

-

b

^

Braids with Edge Effect No: 104 â&#x20AC;&#x201C; One Way Another pattern with the same edge as the previous braid, also the cross-section has a similarity. At steps 3 and 4 pull the active strand a little more to get it in place.

Table 104

1

2

3

4

5

e

1 (5L/4R)

^

-

-

4

-

*

*

-

5

*

*

e

2 (4L/5R) 3 (5L/4R) 4 (4L/5R)

^

-

3

4

d

c

b

a

d

-

-

^

d

c

-

^

Braids with Edge Effect No: 105 â&#x20AC;&#x201C; Twister A third variation on the same edge. Also in this braid you have to pull the active strand well in steps 2 and 3 so that it falls below or above the adjacent strand. Variations on patterns are simple and endless. For example, make this braid with 7 strands by omitting column â&#x20AC;&#x153;eâ&#x20AC;?. This will give a completely different braid.

+

o

+

o

Table 105

1

2

3

4

e

1 (4L/4R)

^

2

3

-

*

*

e

-

*

*

e

2 (3L/5R) 3 (4L/4R) 4 (3L/5R)

^

2

-

o

+

o

+

d

c

b

a

d

c

-

^

d

-

-

^

Bonus No: 106 â&#x20AC;&#x201C; Lefty The collection of braids in this book is certainly not complete; there are many ideas and braids that are waiting for exploration and discovery. In this concluding chapter a hint of some of these.

With the following braid it is the way of braiding that deviates. All the strands remain in the left hand during braiding. This makes it possible to interweave such a braid with strands from the right hand.

Table 106

1

2

3

4

5

(6)

1 (5L)

^

-

3

4

-

*

2 (5L)

^

2

-

-

5

*

Bonus No: 107 â&#x20AC;&#x201C; Duo This is a linked braid design; two 5-strand braids that cross each other twice. The result could have been a standard block braid, were it not for the fact that the direction of one lane is different. Now the result is a braid where the strands seem to behave like pairs. A question immediately arises: at what Diagrams can the direction of rotation of some tracks be reversed? Furthermore, this diagram has only two cells with the same direction of rotation. Is this a freedom to take into account when designing new braids?

+

o

+

o

+

Table 107

1

2

3

4

5

f

1 (5L/5R)

^

-

-

4

-

*

*

-

-

*

*

f

2 (4L/6R) 3 (5L/5R) 4 (4L/6R)

^

2

-

-

o

+

o

+

o

e

d

c

b

a

-

-

-

b

^

-

d

-

-

^

Bonus No: 108 â&#x20AC;&#x201C; Promise Following the previous braid, this is a flat 5-strand braid but braided with strands in pairs.

The entire Diagram, made via the Reversed-Diagram-Method, looks inspiring. Incidentally, the table describes a 10-strand braid the normal way (as in not paired).

x

+

x

+

x

Table 108

1

2

3

4

5

f

1 (5L/5R)

^

2

3

4

-

*

*

f

5

*

*

-

2 (4L/6R) 3 (5L/5R) 4 (4L/6R)

^

-

-

4

+

x

+

x

+

e

d

c

b

a

-

-

c

b

^

-

d

c

b

^

Bonus No: 109 â&#x20AC;&#x201C; Swap Many braids in this book can be made visually elegant by giving the strands of different tracks different colors. It becomes extraordinary when you swap these colors at different points in the braid so that the appearance of the braid changes. Here a solution that hardly disrupts the regularity of a braid, applied to an 8-strand braid. The idea is to replace a crossing of tracks locally with a reversal. While this happens, the positions of the other strands remain the same.

Proceed as follows: Choose two different colors and arrange the strands according to the symbols above the table. Run steps 1 to 4 in the normal way until a desired length is reached. Then go through steps 1, 2, 3b, 4b just 1 time. Continue again with steps 1 to 4.

The new action is hereby indicated in the table with an S: the Swap. At step 3b you start with strand 1 as the active strand. Go under 2 and 3 and swap it with strand 4. Then continue further with strand 4 as the active strand.

NB: In this action, the strands do not turn around each other (a twist like No: 36).

+

o

+

o

Table 109

1

2

3

4

e

1 (4L/4R)

^

2

3

4

*

*

-

-

*

*

e

S

*

*

e

2 (3L/5R) 3 (4L/4R)

^

-

-

4 (3L/5R) 3b (4L/4R) 4b (3L/5R)

^

-

-

o

+

o

+

d

c

b

a

-

-

-

^

d

c

b

^

S

c

b

^

Bonus No: 110 â&#x20AC;&#x201C; Turn It is possible to extend the range of designs with the Diagram Method. When explaining this method, I stated that for various reasons it is desirable that all reversals of tracks are on the outside edges. However, this is not a law of Medes and Persians. Here is a simple example. The "conditions" that this Diagram must meet are more difficult to describe than for Diagrams with all reversals on the outside. This will require more research.

Table 110

1

1 (3L/2R)

2

3

c

^

3

*

*

-

-

*

*

c

2 (2L/3R) 3 (3L/2R) 4 (2L/3R)

^

2

b

a

-

^

^

Bonus No: 111 â&#x20AC;&#x201C; Flip Flop The Diagram of this braid seems point-symmetrical. Nevertheless, during braiding, the 0.5 cells on the left and right edges bulge out and those on the front and back remain small.

See the left diagram.

However, the braid has two stable states. By pulling out the strands of the 0.5 cells at the front and back over a certain length, the braid takes on the shape of the right Diagram.

Although the braid is not surprisingly beautiful, it is interesting because it has two stable appearances. This phenomenon also occurred with braids No: 67 and 68.

x

x

o

Table 111

1

2

3

d

1 (3L/3R)

^

2

3

*

*

d

-

*

*

2 (2L/4R) 3 (3L/3R)

^

-

4 (2L/4R) 5 (3L/3R) 6 (2L/4R)

^

-

o

x

x

c

b

a

-

-

^

d

c

b

^

-

-

b

^

3 *

Bonus No: 112 â&#x20AC;&#x201C; Tic Tac Toe I couldn't resist incorporating this braid in this book. Just like braid No: 109 it contains a Swap. Because this Swap is exactly in the center, a different procedure is required. In steps 1, 2, 5 and 6, the active strand, after braiding, stays in the same bundle (on the other side). It is a straightforward design of the Diagram Method. The design has 0.5 and 1 cells, but is easy to scale up to 1.5 and 2 cells. Braiding with 28 strands will be a challenge though.

o

x

o

+

o

x

Table 112

1

2

3

4

5

6

7

1 (6L/6R)

^

2

3

4

5

-

*

2 (6L/6R) 3 (6L/6R)

^

2

3

-

-

4 (5L/7R) 5 (6L/6R)

6

x

* ^

-

-

-

-

6

8 (5L/7R)

^

-

-

4

5

*

#

x

#

+

#

g

f

e

d

c

b

a

*

f

e

d

c

b

^

-

-

e

-

-

b

^

*

-

-

-

-

-

^

f

-

d

c

-

^

*

*

6 (6L/6R) 7 (6L/6R)

+

x

* g

Bonus No: 113 â&#x20AC;&#x201C; Thin Cell This braid is a worthy end of this book. The Diagram in the Diagram-Method consists of tracks positioned in very narrow loops. Some cells are only 1 unit wide. The finished braid can hardly be recognized in this Diagram (I deliberately omitted a photo).

A similar design with 14 strands and the intersection of narrow loops on the 4th row of the Diagram (instead of the 3rd) also delivers a very captivating braid. Diagrams with narrow loops seem to produce fascinating braids and other designs still seem conceivable. There is still much to discover.

+

o

+

o

+

Table 113

1

2

3

4

5

f

1 (5L/5R)

^

2

3

-

5

*

*

f

5

*

*

-

2 (4L/6R) 3 (5L/5R) 4 (4L/6R)

^

-

3

4

o

+

o

+

o

e

d

c

b

a

e

d

c

-

^

e

-

c

b

^