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In this study, we show that the characteristic radius rs, mass Ms, and the X-ray temperature, TX, of galaxy clusters form a thin plane in the space of (log rs, log Ms, log TX). This tight correlation indicates that the cluster structure including the temperature is affected by the formation time of individual clusters. Numerical simulations show that clusters move along the fundamental plane as they evolve. The plane and the cluster evolution within the plane can be explained by a similarity solution of structure formation. The angle of the plane shows that clusters have not achieved "virial equilibrium". The details of this study are written in Fujita et al. (2018a,b). [ABSTRACT FROM AUTHOR]