432
xkcd #2882: Net Rotations
(imgs.xkcd.com)
Alt text:
For decades I've been working off the accumulated rotation from one long afternoon on a merry-go-round when I was eight.
Three rights make a left. It's entirely possible to have an unbalanced ratio of left to right rotations in a day
Triangular grid guy: "Guess I'm going back the way I came."
Hexagonal grid guy: "What is left. What is right. This did nothing! Nothing!"
Guy on Penrose tiling: "Get me out of here!"
(In before: "You have the first two the wrong way around." Not if they're walking the edges.)