discovered facts:

1.  Each surface intersects the critical capacity slices
in a single loop.

2.  If p1/q1 is an even farey predecessor of p0/q0 then
there is a single loop in the critical slice for p0/q0
which is the principle surface for p1q1.  (copying)

3.  The mass of a surface is defined to be -1 + the
capacity of the min capacity slice it intersects.
A surface of mass M continues in either direction 
until it is blocked by planes of capacity less than M.