The assembly of the β-amyloid peptide, Aβ, into soluble oligomers is associated with neurodegeneration in Alzheimer's disease. The Aβ oligomers are thought to be composed of β-hairpins. Here, the effect of shifting the residue pairing of the β-hairpins on the structures of the oligomers that form is explored through X-ray crystallography. Three residue pairings were investigated using constrained macrocyclic β-hairpins in which Aβ30-36 is juxtaposed with Aβ17-23, Aβ16-22, and Aβ15-21. The Aβ16-22-Aβ30-36 pairing forms a compact ball-shaped dodecamer composed of fused triangular trimers. This dodecamer may help explain the structures of the trimers and dodecamers formed by full-length Aβ.