Nanoclusters usually display exotic physical and chemical properties due to their intriguing geometric structures in contrast to their bulk counterparts.By means of first-principles calculations within density functional theory, we find that heavy noble metal PtN nanoclusters around the size N=55 prefer an open configuration [1], rather than previously reported close-packed icosahedron or core-shell structures [2-3].Specifically, the on-site Coulomb interaction and relativistic effect are identified to significantly reduce the density of states by the Fermi levels upon orbital splitting, and therefore play the key role in stabilizing these structures [1].Particularly, the widely supposed magic cluster size of 55 from the icosahedron construction, is changed to 57 and the corresponding three-atomic-layer structure with D6h symmetry is stabilized by significantly enhanced covalent bindings [1].These findings about PtN clusters are also applicable to IrN clusters, but qualitatively different from their earlier neighboring element Os and their later neighboring element Au [1].The magic numbers for Os and Au are even, being 56 and 58 respectively, as predicted by either a recently established generalized Wulff construction principle [4] or electronic/geometric shell closure models [2-3].