A, Polyhedral geometry is specified. Clockwise from top left: icosahedral, dihedral, octahedral, and tetrahedral geometries are shown. B, An antibody Fc model from hIgG1 is aligned to one of the C2 axes (in this case, a D2 dihedron is shown). C, Antibody Fc-binders are fused to helical repeat proteins that are then fused to the monomeric subunit of helical cyclic oligomers. All combinations of building blocks and building block junctions are sampled (below inset, grey). D, Tripartite fusions are checked to ensure successful alignment of the C2 Fc symmetry axes with that of the polyhedral architecture (in the case of the D2 symmetry shown here, the C2 axes must intersect at a 90° angle). E, Fusions that pass the geometric criteria move forward with sidechain redesign, where e.g. amino acids are optimized to ensure that core-packing residues are nonpolar and solvent-exposed residues are polar. F, Designed AbC-forming oligomers are bacterially expressed, purified, and assembled with antibody Fc or IgG.