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A theoretical method is developed to find isomers of cluster particles, and the isomer spectrum of carbon clusters Cn (n = 3-44) is obtained. It is found that the isomers of 3-11 atoms are in either mono-ring or line shapes,while the isomers of 12-18 atoms show flat sheet shapes. As cluster size increases, bowl isomers become more (n ＞ 19) until cage isomers dominate the structures (n ＞ 27). Based on the isomer spectrum, results of a previous experiment are interpreted.