One of the hallmarks of Alzheimer's disease is the self-assembly of the microtubule-associated protein tau into fibers termed "paired helical filaments" (PHFs). However, the structural basis of PHF assembly at atomic detail is largely unknown. Here, we applied solid-state nuclear magnetic resonance (ssNMR) spectroscopy to investigate in vitro assembled PHFs from a truncated three-repeat tau isoform (K19) that represents the core of PHFs. We found that the rigid core of the fibrils is formed by amino acids V306 to S324, only 18 out of 99 residues, and comprises three beta-strands connected by two short kinks. The first beta-strand is formed by the well-studied hexapeptide motif VQIVYK that is known to self-aggregate in a steric zipper arrangement. Results on mixed [N-15:C-13]-labeled K19 fibrils show that beta-strands are stacked in a parallel, in-register manner. Disulfide bridges formed between C322 residues of different molecules lead to a disturbance of the beta-sheet structure, and polymorphism in ssNMR spectra is observed. In particular, residues K321-S324 exhibit two sets of resonances. Experiments on K19 C322A PHFs further confirm the influence of disulfide bond formation on the core structure. Our structural data are supported by H/D exchange NMR measurements on K19 as well as a truncated four-repeat isoform of tau (K18). Site-directed mutagenesis studies show that single-point mutations within the three different beta-strands result in a significant loss of PHF aggregation efficiency, highlighting the importance of the beta-structure-rich regions for tau aggregation.