I consider this tie to be closer in to the Pratt knot than the Half-Windsor, so why should it be called the co-half-windsor.

I dub thee: The Total Pratt Knot

The co-half-windsor ( Li Ro Ci Ro Li Co T ) is the cousin to the Half-Windsor knot ( Li Ro Ci Lo Ri Co T ). In swapping two moves it remains similar in that it is tied right side out and absurdly considered “mathematically” asymmetrical (same number of L and R moves), but different in that it is visually symmetrical, self-releasing… and completely dismissed everywhere. I believe the visual symmetry is achieved through the obvious symmetry around the first Centring move – Li Ro Ci Ro Li  – nearest the center are Ro moves on either side, followed by Li moves. Note that all knots end with “Co T” (some do have extra loops and are written “Co T T” or even “Co T T T” ) and so that doesn’t affect symmetry (except that it actually does  – the final Co creates visually balancing “ear” on the left (skinny) side of this knot).  Also interesting (and wrong) is that Fink considers that the half windsor to have a balance of 0 (number of times the running part switches from clockwise to counterclockwise or vice versa) and the co-half-windsor to be 1 – this is clearly backwards as the co-half-windsor only moves counterclockwise and never reverses.  

Sadly there are no pictures or diagrams of the co-half-windsor and we have to settle for diagrams of the half-windsor – which in my opinion is an entirely different knot:

The capital letter denotes where the running end moves to –  Left, Right, or Center (between the both the running end standing parts hanging down from the neck) .  The lower case letter denotes if the movement goes Into (i) the page or Out (o) the page.  That’s part is just dumb – it’s backwards unless your are looking at a book. Over (o) or Under (u)  would make more sense to me – works if it’s on a page, in the mirror, or… wait for it… hanging around your neck! Rewriting the co-half-windsor with over or under notation and putting the Over/Under instruction first (as you might speak it) looks like  this: 

oL uR oC uR oL uC T

And would be verbally stated as:

First move the fat part of the tie OVER the LEFT part (oL)

Next move the fat part of the tie UNDER the RIGHT part (uL)

Next move the fat part of the tie OVER the CENTER of the knot (oC)

Next move the fat part of the tie UNDER the RIGHT part (uR)

Next move the fat part of the tie OVER the LEFT part (oL)

Next move the fat part of the tie UNDER the CENTER

Last move the fat part of the tie THROUGH the loop

I often think this might be similar to the “Pratt Knot” / “Shelby Knot” ( Lo Ci Lo Ri Co T ) or the “Nicky Knot” ( Lo Ci Ro Li Co T ).  It is definitely not like the four-in-hand knot ( Li Ro Li Co T ). 

This cousin of the half-Windsor has the advantage of self-releasing (unknotting) when the thin end is pulled out through the knot.

http://www.tcm.phy.cam.ac.uk/~tmf20/tieknots.shtml

7     Li Ro Ci Lo Ri Co T     half-Windsor

If a man claims to know a second knot in addition to the four-in-hand, it is likely to be the half-Windsor, the third of the four classic tie knots. This symmetric knot is medium-sized, with the silhouette of an equilateral triangle. It can satisfactorily be worn with collars of most sizes and spreads. Although the name of the half-Windsor suggests it is derived from the Windsor, there is little direct evidence for this claim. Moreover, the half-Windsor is not half the size of the Windsor, but rather three-quarters.

Keep in mind that the half-Windsor is sometimes a victim of the erroneous naming convention used to describe both it and the Windsor, calling them the Windsor and double-Windsor. There is no such thing as a double Windsor, and the Windsor should be used to refer to knot 31 only.

http://www.tcm.phy.cam.ac.uk/~tmf20/tieknots.shtml

COMPREHENSIVE LIST OF KNOTS

Here is a list of all possible knots, regardless of their aesthetic value. The columns are as follows:

• Number is the number of the knot, and, along with any subscripts or superscripts, a unique identifier (e.g., FM7 is the half-Windsor, where FM refers to the Fink-Mao notation). Knots are ordered first by size, then by the number of centre moves C, then by symmetry s, then by balance b.
• Size is the number of moves, not including T. Higher values correspond to bigger knots.
• Centres is the number of centre moves C. Higher values correspond to broader knots.
• Sequence   The instructions for tying the knot, using the notation described at the top of this page.
• Symmetry (s) is the absolute value of the difference between the number of R and L moves.
• Balance (b) is the number of times the winding of the wide blade switches from clockwise to counter-clockwise, or vice-versa.
• Knotted status (k)   Whether, when the tie is removed over the head and the thin end pulled out of the knot, a knot remains (y) or does not (n). If a knot remains, it is said to be not self-releasing; if no knot remains, it is said to be self-releasing.
• Name   Standard name of the knot.
• 3_on   The subscript on is short for Onassis, and it indicates his particular style of bring the wide blade behind and through the center after tying a four-in-hand. This variation can be applied to any knot but the results are all much the same.
• 3₂, 6₂, etc.   If a knot ends with two Ts, it is subscripted ₂; if three Ts, it is subscripted ₃; and so on.
• 3₂^r, etc.   The superscript r means the tie is worn in reverse, that is, back-to-front. While this is of course possible for any knot, with some it gives unusual and pleasant results. The tie itself should be reversed before tying.

No.	Size	Cen.	Sequence	s	b	k	Name
1	3	1	Lo Ri Co T	0	0	y	Oriental
2	4	1	Li Ro Li Co T	1	1	n	four-in-hand
2on	4	1	Li Ro Li Co T Ri Co	1	1		Onassis
3	5	1	Lo Ri Lo Ri Co T	0	2	y	Kelvin
32	5	1	Lo Ri Lo Ri Co T T	0	2		cross Kelvin
32r	5	1	Lo Ri Lo Ri Co T T	0	2		diagonal
4	5	2	Lo Ci Ro Li Co T	1	0	n	Nicky
5	5	2	Lo Ci Lo Ri Co T	1	1	y	Pratt
6	6	1	Li Ro Li Ro Li Co T	1	3	n	Victoria
62	6	1	Li Ro Li Ro Li Co T T	1	3		cross Victoria
7	6	2	Li Ro Ci Lo Ri Co T	0	0	y	half-Windsor
8	6	2	Li Ro Ci Ro Li Co T	0	1	n	co-half-Windsor
9	6	2	Li Co Ri Lo Ri Co T	0	1	y
10	6	2	Li Co Li Ro Li Co T	2	2	n
11	7	1	Lo Ri Lo Ri Lo Ri Co T	0	4	y
112	7	1	Lo Ri Lo Ri Lo Ri Co T T	0	4
113	7	1	Lo Ri Lo Ri Lo Ri Co T T T	0	4
12	7	2	Lo Ri Lo Ci Ro Li Co T	1	1	n	St Andrew
13	7	2	Lo Ri Co Li Ro Li Co T	1	1	n
14	7	2	Lo Ri Lo Ci Lo Ri Co T	1	2	y	co-St Andrew
15	7	2	Lo Ri Co Ri Lo Ri Co T	1	2	y
16	7	2	Lo Ci Ro Li Ro Li Co T	1	2	n
162	7	2	Lo Ci Ro Li Ro Li Co T T	1	2
17	7	2	Lo Ci Lo Ri Lo Ri Co T	1	3	y
172	7	2	Lo Ci Lo Ri Lo Ri Co T T	1	3
18	7	3	Lo Ci Ro Ci Lo Ri Co T	0	1	y	Plattsburgh
19	7	3	Lo Ci Ro Ci Ro Li Co T	0	2	n	co-Plattsburgh
20	7	3	Lo Ci Lo Ci Ro Li Co T	2	2	n
21	7	3	Lo Ci Lo Ci Lo Ri Co T	2	3	y
22	8	1	Li Ro Li Ro Li Ro Li Co T	1	5	n
222	8	1	Li Ro Li Ro Li Ro Li Co T T	1	5
223	8	1	Li Ro Li Ro Li Ro Li Co T T T	1	5
23	8	2	Li Ro Li Co Ri Lo Ri Co T	0	2	y	Cavendish
24	8	2	Li Ro Li Ro Ci Lo Ri Co T	0	2	y
25	8	2	Li Ro Ci Lo Ri Lo Ri Co T	0	2	y
252	8	2	Li Ro Ci Lo Ri Lo Ri Co T T	0	2		Christensen
26	8	2	Li Ro Li Ro Ci Ro Li Co T	0	3	n
27	8	2	Li Ro Ci Ro Li Ro Li Co T	0	3	n
272	8	2	Li Ro Ci Ro Li Ro Li Co T T	0	3		co-Christensen
28	8	2	Li Co Ri Lo Ri Lo Ri Co T	0	3	y
282	8	2	Li Co Ri Lo Ri Lo Ri Co T T	0	3
29	8	2	Li Ro Li Co Li Ro Li Co T	2	3	n
30	8	2	Li Co Li Ro Li Ro Li Co T	2	4	n
302	8	2	Li Co Li Ro Li Ro Li Co T T	2	4
31	8	3	Li Co Ri Lo Ci Ro Li Co T	1	0	n	Windsor
32	8	3	Li Co Li Ro Ci Lo Ri Co T	1	1	y	co-Windsor 1
33	8	3	Li Co Ri Lo Ci Lo Ri Co T	1	1	y	co-Windsor 2
34	8	3	Li Ro Ci Lo Ci Ro Li Co T	1	1	n
35	8	3	Li Co Li Ro Ci Ro Li Co T	1	2	n	co-Windsor 3
36	8	2	Li Ro Ci Ro Ci Lo Ri Co T	1	2	y
37	8	3	Li Ro Ci Lo Ci Lo Ri Co T	1	2	y
38	8	3	Li Co Ri Co Li Ro Li Co T	1	2	n
39	8	3	Li Ro Ci Ro Ci Ro Li Co T	1	3	n
40	8	3	Li Co Li Co Ri Lo Ri Co T	1	3	y
41	8	3	Li Co Ri Co Ri Lo Ri Co T	1	3	y
42	8	3	Li Co Li Co Li Ro Li Co T	3	4	n
43	9	1	Lo Ri Lo Ri Lo Ri Lo Ri Co T	0	6	y
432	9	1	Lo Ri Lo Ri Lo Ri Lo Ri Co T T	0	6
433	9	1	Lo Ri Lo Ri Lo Ri Lo Ri Co T T T	0	6
434	9	1	Lo Ri Lo Ri Lo Ri Lo Ri Co T T T T	0	6
44	9	2	Lo Ri Lo Ri Co Li Ro Li Co T	1	3	n	Granchester
45	9	2	Lo Ri Lo Ci Ro Li Ro Li Co T	1	3	n
452	9	2	Lo Ri Lo Ci Ro Li Ro Li Co T T	1	3
46	9	2	Lo Ri Lo Ri Lo Ci Ro Li Co T	1	3	n
47	9	2	Lo Ri Co Li Ro Li Ro Li Co T	1	3	n
472	9	2	Lo Ri Co Li Ro Li Ro Li Co T T	1	3
48	9	2	Lo Ri Lo Ri Co Ri Lo Ri Co T	1	4	y	co-Grantchester
49	9	2	Lo Ri Lo Ci Lo Ri Lo Ri Co T	1	4	y
492	9	2	Lo Ri Lo Ci Lo Ri Lo Ri Co T T	1	4
50	9	2	Lo Ri Lo Ri Lo Ci Lo Ri Co T	1	4	y
51	9	2	Lo Ri Co Ri Lo Ri Lo Ri Co T	1	4	y
512	9	2	Lo Ri Co Ri Lo Ri Lo Ri Co T T	1	4
52	9	2	Lo Ci Ro Li Ro Li Ro Li Co T	1	4	n
522	9	2	Lo Ci Ro Li Ro Li Ro Li Co T T	1	4
523	9	2	Lo Ci Ro Li Ro Li Ro Li Co T T T	1	4
53	9	2	Lo Ci Lo Ri Lo Ri Lo Ri Co T	1	5	y
532	9	2	Lo Ci Lo Ri Lo Ri Lo Ri Co T T	1	5
533	9	2	Lo Ci Lo Ri Lo Ri Lo Ri Co T T T	1	5
54	9	3	Lo Ri Co Li Ro Ci Lo Ri Co T	0	0	y	Hanover
55	9	3	Lo Ri Co Ri Lo Ci Ro Li Co T	0	1	n	co-Hanover 1
56	9	3	Lo Ri Co Li Ro Ci Ro Li Co T	0	1	n	co-Hanover 2
57	9	3	Lo Ci Ro Li Ro Ci Lo Ri Co T	0	1	y
58	9	3	Lo Ci Ro Li Co Ri Lo Ri Co T	0	1	y	co-Hanover 3
59	9	3	Lo Ri Co Ri Lo Ci Lo Ri Co T	0	2	y
60	9	3	Lo Ci Ro Li Ro Ci Ro Li Co T	0	2	n
61	9	3	Lo Ri Lo Ci Ro Ci Lo Ri Co T	0	2	y
62	9	3	Lo Ri Co Li Co Ri Lo Ri Co T	0	2	y
63	9	3	Lo Ri Lo Ci Ro Ci Ro Li Co T	0	3	n
64	9	3	Lo Ri Co Ri Co Li Ro Li Co T	0	3	n
65	9	3	Lo Ci Lo Ri Co Ri Lo Ri Co T	0	3	y
66	9	3	Lo Ci Ro Ci Lo Ri Lo Ri Co T	0	3	y
662	9	3	Lo Ci Ro Ci Lo Ri Lo Ri Co T T	0	3
67	9	3	Lo Ci Ro Ci Ro Li Ro Li Co T	0	4	n
672	9	3	Lo Ci Ro Ci Ro Li Ro Li Co T T	0	4
68	9	3	Lo Ci Lo Ri Lo Ci Ro Li Co T	2	2	n
69	9	3	Lo Ci Lo Ri Co Li Ro Li Co T	2	2	n
70	9	3	Lo Ci Ro Li Co Li Ro Li Co T	2	2	n
71	9	3	Lo Ci Lo Ri Lo Ci Lo Ri Co T	2	3	y
72	9	3	Lo Ri Lo Ci Lo Ci Ro Li Co T	2	3	n
73	9	3	Lo Ri Co Li Co Li Ro Li Co T	2	3	n
74	9	3	Lo Ri Lo Ci Lo Ci Lo Ri Co T	2	4	y
75	9	3	Lo Ri Co Ri Co Ri Lo Ri Co T	2	4	y
76	9	3	Lo Ci Lo Ci Ro Li Ro Li Co T	2	4	n
762	9	3	Lo Ci Lo Ci Ro Li Ro Li Co T T	2	4
77	9	3	Lo Ci Lo Ci Lo Ri Lo Ri Co T	2	5	y
772	9	3	Lo Ci Lo Ci Lo Ri Lo Ri Co T T	2	5
78	9	4	Lo Ci Ro Ci Lo Ci Ro Li Co T	1	2	n	Balthus
79	9	4	Lo Ci Lo Ci Ro Ci Lo Ri Co T	1	3	y
80	9	4	Lo Ci Ro Ci Ro Ci Lo Ri Co T	1	3	y
81	9	4	Lo Ci Ro Ci Lo Ci Lo Ri Co T	1	3	y	co-Balthus
82	9	4	Lo Ci Lo Ci Ro Ci Ro Li Co T	1	4	n
83	9	4	Lo Ci Ro Ci Ro Ci Ro Li Co T	1	4	n
84	9	4	Lo Ci Lo Ci Lo Ci Ro Li Co T	3	4	n
85	9	4	Lo Ci Lo Ci Lo Ci Lo Ri Co T	3	5	y

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