Nanoparticles of (CdSe)n are found extremely stable at n = 33 and 34 with structures distinctively different from the bulk fragments. They grow exclusively in large amount with a simple solution method. The diameter is determined as 1.5 nm. Such ultra-stable nanoparticles had been predicted both theoretically and experimentally after the discovery of carbon fullerenes, but not been produced macroscopically in any other element or compound system. First-principles calculations predict that the structures of (CdSe)33 and (CdSe)34 are puckered (CdSe)28-cages accommodating respectively (CdSe)5 an (CdSe)6 inside to form a three-dimensional network of essentially hetero-polar sp3-bonding. {\textcopyright} EDP Sciences, Societ{\`{a}} Italiana di Fisica, Springer-Verlag 2005.