Polyadic, or "multicast" social interaction networks arise when one sender addresses multiple receivers simultaneously. Currently available relational event models (REM) are not well suited to the analysis of polyadic interaction networks because they specify event rates for sets of receivers as functions of dyadic covariates associated with the sender and one receiver at a time. Relational hyperevent models (RHEM) address this problem by specifying event rates as functions of hyperedge covariates associated with the sender and the entire set of receivers. For instance, hyperedge covariates can express the tendency of senders to repeatedly address the same pairs (or larger sets) of receivers - a simple and frequent pattern in polyadic interaction data which, however, cannot be expressed with dyadic covariates. In this article we demonstrate the potential benefits of RHEMs for the analysis of polyadic social interaction. We define and discuss practically relevant effects that are not available for REMs but may be incorporated in empirical specifications of RHEM. We illustrate the empirical value of RHEM, and compare them with related REM, in a reanalysis of the canonical Enron email data.