Ab initio calculations on Rhn(n=8-64) clusters surprisingly show simple cubic structures to be most favorable up to n∼27. These are stabilized by eight center bonding and lie significantly lower in energy than the icosahedral isomers found in previous studies. With increasing size cuboctahedral, decahedral and icosahedral isomers become preferred, showing a reversal of the growth behavior compared with the well-known icosahedral→decahedral→ cuboctahedral transitions. The low-coordination cubic structures have lower magnetic moments than the dense packed icosahedral isomers and which agree closely with experiments. Our results resolve a long standing discrepancy between theory and experiments and provide a new direction in the understanding of the properties of transition metal clusters. {\textcopyright} 2005 The American Physical Society.