In social tagging systems, also known as folksonomies, users collaboratively manage tags to annotate resources. Naturally, social tagging systems can be modeled as a tripartite hypergraph, where there are three different types of nodes, namely users, resources and tags, and each hyperedge has three end nodes, connecting a user, a resource and a tag that the user employs to annotate the resource. Then, how can we automatically detect user, resource and tag communities from the tripartite hypergraph? In this paper, by turning the problem into a problem of finding an efficient compression of the hypergraph's structure, we propose a quality function for measuring the goodness of partitions of a tripartite hypergraph into communities. Later, we develop a fast community detection algorithm based on minimizing the quality function. We explain advantages of our method and validate it by comparing with various state of the art techniques in a set of synthetic datasets.