No, they put a low-poly mesh into the algorithm (I presume so it'd be foldable in a reasonable amount of time). "Maybe links some of the triangles together" is

No, they put a low-poly mesh into the algorithm (I presume so it'd be foldable in a reasonable amount of time). "Maybe links some of the triangles together" is the difficult part, especially since they guarantee the boundary of the paper folds to the boundary of the mesh.