Polycomb repressive complex 2 (PRC2) installs and spreads repressive histone methylation marks on eukaryotic chromosomes. Because of the key roles that PRC2 plays in development and disease, how this epigenetic machinery interacts with DNA and nucleosomes is of major interest. Nonetheless, the mechanism by which PRC2 engages with native-like chromatin remains incompletely understood. In this work, we employ single-molecule force spectroscopy and molecular dynamics simulations to dissect the behavior of PRC2 on polynucleosome arrays. Our results reveal an unexpectedly diverse repertoire of PRC2 binding configurations on chromatin. Besides reproducing known binding modes in which PRC2 interacts with bare DNA, mononucleosomes, and adjacent nucleosome pairs, our data also provide direct evidence that PRC2 can bridge pairs of distal nucleosomes. In particular, the "1-3" bridging mode, in which PRC2 engages two nucleosomes separated by one spacer nucleosome, is a preferred low-energy configuration. Moreover, we show that the distribution and stability of different PRC2-chromatin interaction modes are modulated by accessory subunits, oncogenic histone mutations, and the methylation state of chromatin. Overall, these findings have implications for the mechanism by which PRC2 spreads histone modifications and compacts chromatin. The experimental and computational platforms developed here provide a framework for understanding the molecular basis of epigenetic maintenance mediated by Polycomb-group proteins.