Using ab initio methods, we investigate the structural evolution of a family of gold-sulfide cluster anions (Au(m)S(n)(-)). We show that this family of clusters exhibits simple size-evolution rules and novel hollow polyhedron structures. The highly stable Au(m)S(n)(-) species such as Au(6)S(4)(-), Au(9)S(5)(-), Au(9)S(6)(-), Au(10)S(6)(-), Au(11)S(6)(-), Au(12)S(8)(-), and Au(13)S(8)(-) detected in the recent ion mobility mass spectrometry experiment of Au(25)(SCH(2)CH(2)Ph)(18) (Angel et al. ACS Nano2010, 4, 4691) are found to possess either quasi-tetrahedron, pyramidal, quasi-triangular prism, or quasi-cuboctahedron structures. The formation of these polyhedron structures are attributed to the high stability of the S-Au-S structural unit. A unique "edge-to-face" growth mechanism is proposed to understand the structural evolution of the small Au(m)S(n)(-) cluster. A 3:2 ratio rule of Au/S is suggested for the formation of a hollow polyhedron structure among small-sized Au(m)S(n) clusters.