Semiregular models are an important subset of models in computer graphics. They are typically obtained by applying repetitive regular refinements on an initial arbitrary model. As a result, their connectivity strongly resembles regularity due to these refinement operations. Although data structures exist for regular or irregular models, a data structure designed to take advantage of this semiregularity is desirable. In this paper, we introduce such a data structure called atlas of connectivity maps for semiregular models resulting from arbitrary refinements. This atlas maps the connectivity information of vertices and faces on separate 2D domains called connectivity maps. The connectivity information between adjacent connectivity maps is determined by a linear transformation between their 2D domains. We also demonstrate the effectiveness of our data structure on subdivision and multiresolution applications.