Stand in front of the mirror with your tie around your neck. The thick end should be in your right hand and the thin end in your left hand.
In the interest of clarity I will henceforth refer to the thick end as 'T' and the thin end as 't'.
After the first phase of tie manipulation (FPTM), we will obviously need to differentiate between the working ends and the original ends, which will still, from time to time, be in play. To this end I will refer to the new working ends as T1 and t1, and after the second phase of tie manipulation (SPTM), T2 and t2. Third phase, T3 and t3 and so on and so forth.
You will by now no doubt have noticed that the mirror image has T where t should be and t where T should be. In the interest of clarity, when refering to the mirror image I will of course use T(m), t(m), T1(m), t1(m), and so on and soforth.
Now then, flop T over t.
Make a cup of tea. This could take a while.