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In this paper, we follow up on the studies developed by Kovalevsky (Comput Vis Graph Image Process 46:141-161, ) and Kenmochi et al. (Comput Vis Image Underst 71:281-293, ), which defined a continuous analog for a 4-dimensional digital object. Here, we construct a cell complex that has the same topological information as the original 4-dimensional digital object. [ABSTRACT FROM AUTHOR]