In Tsubaki America's haiden (if I'm recalling correctly) there is a picture of triangle circle and square which goes left to right, respectively. On the web page it also is shown in that format. I can see how it might go right to left given the direction of Japanese writing, but I couldn't say very well. Considering as a group they seem to represent a kind of unitary principle, I can see how there might not always be a fixed order. Looking at the physical symbolism of gas, liquid, and solid, depending on whether you're warming up or cooling down, you move from one "direction" to another, for example.
Hopefully people with a better understanding will be able to shed a more definate light on the subject...oops didn't see Chris's post when I started this: there ya go.