Single-phase K8Sn25 is synthesized from the elements on annealing below 400 degrees C. The phase is somewhat nonstoichiometric, and the lattice constant also depends on thermal history. The structure was solved for K-7.4(1-)Sn-25 (s.g. P4(1)32, Z = 4, a = 16.294(5) Angstrom, R/R(w) = 4.0/3.6% for 833 observed reflections and 55 parameters). The new structure type contains pentagonal dodecahedra of tin that share three pentagonal faces with like members and are also interconnected to another cage through a single exo bond. Tin-tin distances are very similar to those in gray tin and in Rb8Sn44. The three types of potassium ions are (1) encapsulated in each Sn-20 cage, (2) bonded in tin octahedra between clusters, and (3) somewhat disordered in channels through the tin network. Eight tin atoms per formula unit are three-bonded, the remainder four-bonded, and the ideal compositon K8.0Sn25 is, appropriately, a diamagnetic semiconductor. An analogous compound does not form in the binary rubidium or cesium-systems. The crystal structures of the isostructural Rb8Sn44.6(1) and K-1.6(2)Cs-6.4(2)Sn-44.0(1) were also refined (Pm3n, Z = 1, a = 12.054(1), 12.084(1) Angstrom, R/R(w) = 7.6/6.7, 6.6/5.7, respectively). These are defect members of the clathrate-I A(8)(H2O)(46) type structure with one-third random vacancies at the 6c positions and classical Zintl phases. K8Sn44 was shown to be a diamagnetic semiconductor.