Concise representations of frequent itemsets sacrifice readability and direct interpretability by a data analyst of the concise patterns extracted. In this paper, we introduce an extension of itemsets, called regular, with an immediate semantics and interpretability, and a conciseness comparable to closed itemsets. Regular itemsets allow for specifying that an item may or may not be present; that any subset of an itemset may be present; and that any non-empty subset of an itemset may be present. We devise a procedure, called RegularMine, for mining a set of regular itemsets that is a concise representation of frequent itemsets. The procedure computes a covering, in terms of regular itemsets, of the frequent itemsets in the class of equivalence of a closed one. We report experimental results on several standard dense and sparse datasets that validate the proposed approach.