I started answering a question on the SCA-Card-Weaving email list, but the answer quickly got too complicated for easy emailing, and I thought it might be interesting to others as well.
The question: “Is flipping a card on its vertical axis really the same as reversing the direction? That is, instead of FF -flip- FF can I turn FFBB? Will it work if there are three colors so the card isn’t symmetrical?”
The answer: sure!
Let’s invoke ASCII art:
Say you have a card threaded with three colors: A, B and C. Let’s say that it is Z-threaded, so that when you turn it forward the diagonal *in the band* is S-ways.
band A B warp C A
So then if you turn the card forward, the thread that crosses the top is the one that shows. So after the first turn forward an A thread will show in the band, and it will be at an S angle in the band. Second one will be C.
A C C A B S S Z Z Z A B -F- C A -F- A C -B- C A -B- A B -B- B A C A A B B A A B C A A C
If you turn the card FFBBB then it will be ACCAB at SS then ZZZ angle (see how the colors are symmetrical where the reversal happens?)
But what if you flip the card on its vertical axis instead?
A C C A B S S Z Z Z A B -F- C A -F- A C -FLIP- C A -F- A C -F- B A -F- A B C A A B B A | A B B A A C C A
Lovely: ACCAB at SSZZZ angles in the band. Your results should look identical with either method.