The assembly of nucleic acid nanostructures with controlled size and shape has large impact in the fields of nanotechnology, nanomedicine and synthetic biology. The directed arrangement of nanostructures at interfaces is important for many applications. In spite of this, the use of laterally mobile lipid bilayers to control RNA three-dimensional nanostructure formation on surfaces remains largely unexplored. Here, we direct the self-assembly of RNA building blocks into three-dimensional structures of RNA on fluid lipid bilayers composed of cationic 1,2-dioleoyl-3-trimethylammonium-propane (DOTAP) or mixtures of zwitterionic 1,2-dioleoyl-sn-glycero-3-phosphatidylcholine (DOPC) and cationic sphingosine. We demonstrate the stepwise supramolecular assembly of discrete building blocks through specific and selective RNA-RNA interactions, based on results from quartz crystal microbalance with dissipation (QCM-D), ellipsometry, fluorescence recovery after photobleaching (FRAP) and total internal reflection fluorescence microscopy (TIRF) experiments. The assembly can be controlled to give a densely packed single layer of RNA polyhedrons at the fluid lipid bilayer surface. We show that assembly of the 3D structure can be modulated by sequence specific interactions, surface charge and changes in the salt composition and concentration. In addition, the tertiary structure of the RNA polyhedron can be controllably switched from an extended structure to one that is dense and compact. The versatile approach to building up three-dimensional structures of RNA does not require modification of the surface or the RNA molecules, and can be used as a bottom-up means of nanofabrication of functionalized bio-mimicking surfaces.