Formal concept analysis is a mathematical framework based on lattice theory that aims at representing the information contained in binary object-attribute datasets (called formal contexts) in the form of a lattice of so-called formal concepts. Since its introduction, it has been extended to more complex types of data. In this paper, we are interested in two of those extensions: relational concept analysis and polyadic concept analysis that allow to process, respectively, relational data and $n$-ary relations. We present a framework for polyadic relational concept analysis that extends relational concept analysis to relational datasets that are made of $n$-ary relations. We show its basic properties and that it is a valid extension of relational concept analysis.