We present a detailed analysis of IC 4776, a planetary nebula displaying a morphology believed to be typical of central star binarity. The nebula is shown to comprise a compact hourglass-shaped central region and a pair of precessing jet-like structures. Time-resolved spectroscopy of its central star reveals a periodic radial velocity variability consistent with a binary system. Whilst the data are insufficient to accurately determine the parameters of the binary, the most likely solutions indicate that the secondary is probably a low-mass main-sequence star. An empirical analysis of the chemical abundances in IC 4776 indicates that the common-envelope phase may have cut short the asymptotic giant branch evolution of the progenitor. Abundances calculated from recombination lines are found to be discrepant by a factor of approximately 2 relative to those calculated using collisionally excited lines, suggesting a possible correlation between low-abundance discrepancy factors and intermediate-period post-common-envelope central stars and/or Wolf-Rayet central stars. The detection of a radial velocity variability associated with the binarity of the central star of IC 4776 may be indicative of a significant population of (intermediate-period) post-common-envelope binary central stars that would be undetected by classic photometric monitoring techniques.