This proposal is part of our research programme on spin and orbital order in frustrated systems. AgNiO2 has a layered crystal structure with Jahn-Teller active Ni3+ ions forming an antiferromagnetic triangular lattice in the basal plane. Both spin and orbital order are frustrated in this geometry and unusual ground states may occur. There are two structural polytypes which differ in the stacking of NiO2 layers. We have observed a complex supercell structure in the hexagonal polytype with a novel stripe ordered magnetic ground state. Surprisingly the orbital degeneracy is lifted not by Jahn-Teller distortions as in other triangular spin-orbital systems but by charge order. Here we wish to explore the structural distortion lifting the orbital degeneracy in the rhombohedral polytype, where interlayer interactions are different and a new electronic ground state is expected.