Many unrelated proteins and peptides can assemble into amyloid or amyloid-like nanostructures, all of which share the cross-beta motif of repeat arrays of beta-strands hydrogen-bonded along the fibril axis. Yet, paradoxically, structurally polymorphic fibrils may derive from the same initial polypeptide sequence. Here, solid-state nuclear magnetic resonance (SSNMR) analysis of amyloid-like fibrils of the peptide hIAPP(20-29), corresponding to the region S(20)NNFGAILSS(29) of the human islet amyloid polypeptide amylin, reveals that the peptide assembles into two amyloid-like forms, (1) and (2), which have distinct structures at the molecular level. Rotational resonance SSNMR measurements of C-13 dipolar couplings between backbone F23 and 126 of hIAPP(20-29) fibrils are consistent with form (1) having parallel beta-strands and form (2) having antiparallel strands within the beta-sheet layers of the protofilament units. Seeding hIAPP(20-29) with structurally homogeneous fibrils from a 30-residue amylin fragment (hIAPP(8-37)) produces morphologically homogeneous fibrils with similar NMR properties to form (1). A model for the architecture of the seeded fibrils is presented, based on the analysis of X-ray fiber diffraction data, combined with an extensive range of SSNMR constraints including chemical shifts, torsional angles, and interatomic distances. The model features a cross-beta spine comprising two beta-sheets with an interface defined by residues F23, A25, and L27, which form a hydrophobic zipper. We suggest that the energies of formation for fibril form containing antiparallel and parallel beta-strands are similar when both configurations can be stabilized by a core of hydrophobic contacts, which has implications for the relationship between amino acid sequence and amyloid polymorphism in general.