  In this article I show that every special Lagrangian cone in C^3 determines,
and is determined by, a primitive harmonic surface in the 6-symmetric space
SU_3/SO_2. For cones over tori, this allows us to use the classification theory
of harmonic tori to describe the construction of all the corresponding special
Lagrangian cones. A parameter count is given for the space of these, and some
examples found recently by Joyce are put into this context.
