To Engineer is Human: The 85+ Ways to Tie a Tie, now in Technicolor! (Knots 1 to 3)

In 1999, researchers Thomas Fink and Yong Mao at Cambridge University published a book entitled The 85 Ways to Tie a Tie. They came up with a number of criteria to limit their list of possible knots and actually published a pair of research papers on the subject in Nature and Physica A.

Not to be outdone, and disappointed that Fink and Mao ignored some pretty cool looking knots, a group of mathematicians eliminated most of the restrictions Fink and Mao had used and in 2014 published a paper proving that there were actually 177,147 ways to tie a necktie. However, even the authors had to admit that many of their knots were not very aesthetic, so it seems the criteria of Fink and Mao were not unreasonable, even if they did exclude a few good knots.

I've got a decent collection of ties and like to experiment with knots, so I've decided to work my way through all the Fink-Mao knots (plus many of the excluded knots) in this series of posts on tie knots. Click here to see a list of all the knots I've documented.

In this post I bring you knots 1 through 3, plus several variations. Almost all knots can be tied to look like the Onassis knot by either dropping the "T" from the end of the sequence of moves, or (more securely) by adding either "Li Co" or "Ri Co" to the end of the sequence. Knots can also be tied to show off what the back of the knot looks like by mirroring all the moves. Some knots look interesting in reverse and I will occasionally wear a reversed knot just to be different. I will be using the Fink-Mao notation to describe how the knots are tied. If you are unfamiliar with the notation, click on the link provided to get caught up.

Knot 1

Better known as: Small knot, Oriental knot, Kent knot

How it's tied: Lo Ri Co T

Additional notes:

Smallest of all the tie knots.
Narrow end usually extends past the wide end and will have to be hidden in some way. I usually tuck the narrow end into my shirt.
Looks bad when paired with a spread collar because the collar space is way too big.
I find that it tends to loosen easily due to having so few moves holding it together.

What it looks like:

Kent knot (Lo Ri Co T)

Variations:

Onassis ending, loose (Lo Ri Co)
Onassis ending, secure (Lo Ri Co T Li Co)
Reversed knot (Ri Lo Ci T)

Kent knot, Onassis variant (Lo Ri Co)

Kent knot, Onassis variant (Lo Ri Co T Li Co)

Reverse Kent knot (Ri Lo Ci T)

Knot 2

Better known as: Four-in-hand knot, Simple knot, Schoolboy knot

How it's tied: Li Ro Li Co T

Additional notes:

Difficult to make it look symmetrical. If you like symmetry you should probably stick to other knots.
A popular knot to wear loose with the collar button open.

What it looks like:

Four-in-hand knot (Li Ro Li Co T)

Variations:

Onassis ending, loose (Li Ro Li Co)
Onassis ending, secure (Li Ro Li Co T Ri Co). Most references to "Onassis knot" are referring to this particular knot.
Reversed knot (1/2 twist Ro Li Ro Ci T). A half twist is required before the first move in order to hide the tie's seam.