> but the order of the long branches
> should be the same, and you cannot
> rotate the tree.

So 'order' has nothing to do with the geometrical length, right?  It is the depth of the tree that you are talking about?

It seems that the identity of a junction is its angular order (0 <= j < n), its position in the tree (using some traversal), and the quadrant of the complex plain it inhabits.  It seems like the quadrant is totally determined by the angular order (j in my diagram):  

{ { (n/4 <= j < n/2) (-/+), (j < n/4) (+/+) },
{ (n/2 <= j < 3n/4) (-/-) , (3n/4 < j < n) (+/-)} }