It was printed on a makerbot replicator at school, with no supports.
First, I coordinatized the vertices of a single hexagon, plus the five lines inside. The coordinatization was in R2 in the x-y plane.
I defined lines connecting each vertex with a loop that translated multiple spheres along the lines. I used the vector equation of a line: V = v0 + t(v1 - v0), where v0 and v1 are the two vertices on either end of the line.
I re-parameterized each line into toroidal coordinates in order to pop each line out onto the surface of a torus.
After I had the first pattern on the torus, I was able to rotate and copy the pattern all the way around the torus.