Surface solitons in trilete lattices

► Surface soliton complexes in trilete lattices coupled in one site are investigated. ► Symmetric, asymmetric and antisymmetric complexes are found. ► Existence region and stability of complexes is studied numerically and analytically. ► The symmetry-breaking bifurcation is found. ► Creation of the asymmetric branch coincides with destabilization of the symmetric branch.