Deformable fidget spinner is a popular toy, and its multi-chain and deformable advantages provide a solution for space robots. Inspired by this toy, this paper introduces a multi-chain reconfigurable modular robot by combining the flexible and versatile characteristics of chain robots. Topological configurations of multi-chain reconfigurable modular robots are investigated with a focus on configuration analysis and configuration transformation strategies, enabling them to change their topological configurations to suit different tasks. Firstly, combined with integer splitting and permutations, a library of basic non-isomorphic configurations for modular robots with positive hexagonal bases is established, and a non-isomorphic configuration enumeration algorithm is proposed, which shows that the number of non-isomorphic configurations grows exponentially with the number of modules. Secondly, a configuration matching reconfiguration strategy is designed to optimally match and convert between configurations by defining a library of equivalence relations based on structural features, with configuration conversion as the core. Finally, the effectiveness of the reconfiguration strategy is verified through demonstration and simulation.