New low-energy atomic structures and properties of medium-size gold nanoparticles (Au33-42) are studied, where the atomic positions of gold atoms are obtained on the basis of the generic formulation of shell and core concept. Hollow cage, tube-like, double-layered flat, fcc-like, and close-packed configurations are predicted. Relativistic density functional theory optimization indicated that low-symmetry stuffed configurations are all lower in energy than the others. Further analysis of the optimized structures of Au33-42 nanoparticles shows that these gold cores are all four-atom tetrahedral structures and similar to each other; only the number and positions of gold atoms at the surface of gold core are different. Compared with structure and electronic properties, Au33-42 nanoparticles have different structure stabilities and chemical activities. But they are all hybridizations of sp and d electrons. The obtained information forms the basis for future chemisorption studies to unravel the catalytic effects of gold nanoparticles.