The structures of medium sized tin cluster anions Sn(n)(-) (n = 16-29) were determined by a combination of density functional theory, trapped ion electron diffraction and collision induced dissociation (CID). Mostly prolate structures were found with a structural motif based on only three repeatedly appearing subunit clusters, the Sn(7) pentagonal bipyramid, the Sn(9) tricapped trigonal prism and the Sn(10) bicapped tetragonal antiprism. Sn(16)(-) and Sn(17)(-) are composed of two face connected subunits. In Sn(18)(-)-Sn(20)(-) the subunits form cluster dimers. For Sn(21)(-)-Sn(23)(-) additional tin atoms are inserted between the building blocks. Sn(24)(-) and Sn(25)(-) are composed of a Sn(9) or Sn(10) connected to a Sn(15) subunit, which closely resembles the ground state of Sn(15)(-). Finally, in the larger clusters Sn(26)(-)-Sn(29)(-) additional bridging atoms again connect the building blocks. The CID experiments reveal fission as the main fragmentation channel for all investigated cluster sizes. This rather unexpected "pearl-chain" cluster growth mode is rationalized by the extraordinary stability of the building blocks.