The hydrothermal synthesis of the purely inorganic open-framework indium selenide (NH(4))(4)In(12)Se(20) (1) is reported. Compound 1 exhibits a unique three-dimensional open-framework structure. The framework of 1 shows an unusual, for a chalcogenide compound, rigidity arising from the unprecedented connection mode of its building blocks. Compound 1 possesses ion exchange capacity for Cs(+), Rb(+), NH(4) (+), but it has selectivity against Na(+) and Li(+). It also showed exceptional stability in relatively concentrated hydrochloric acid. Ion exchange of 1 with hydrochloric water solutions can produce its solid acid analogue H(2)(NH(4))(2)In(12)Se(20). The maximum cation-exchange capacity of 1 was found equal to two equivalents per mol, which is consistent with an exchange mechanism taking place in the 1D-channels formed by the largest cavities. In addition, 1 can do ion-exchange with heavy-metal ions like Hg(2+), Pb(2+), and Ag(+). The capacity of 1 to clean water solutions from heavy-metal ions was preliminarily investigated and found very high. Specifically, 1 can remove 99.9 % of Hg(2+), 99.8 % of Ag(+), and 94.9 % of Pb(2+) from aqueous solutions of each of these ions. Using different synthetic conditions, we isolated compound (NH(4))(2)In(12)Se(19) (2), which also has as good an acid stability as 1, but no ion-exchange properties. Overall, this work provides new hydrothermal synthetic approaches for isolation of all-inorganic open-framework chalcogenides.