The Ti5S53- union has been obtained by extracting KTlSe in ethylenediamine in the presence of 2,2,2-crypt. The salt, (2,2,2-erypt-K+)(3)Tl5Se53-, crystallizes in the triclinic system, space group P1, with Z = 2 and a = 11.676(2) Angstrom, b = 16.017(3) Angstrom, c = 25.421(5) Angstrom, alpha = 82.32(3)degrees, beta = 88.47(3)degrees, gamma = 69.03(3)degrees at -123 degreesC. Two other mixed oxidation stale Tl-I/Tl-III unions, Tl4Se54- and Tl4Se64-, have been obtained by extracting KTlSe into liquid NH3 in the presence of 2,2,2-crypt and have been characterized in solution by low-temperature Se-77, Tl-203, and Tl-205 NMR soectroscopy and were shown to exist as a 1:1 equilibrium mixture at -40 degreesC. The couplings, (1)J(Tl-203.205-Se-77) and (2)J((Tl-203.205Tl)-Tl-203.205), have been observed for Tl4Se54- and Tl4Se64- and have been used to arrive at the solution structures of both anions. Structural assignments achieved by de: were achieved by detailed analyses and simulations of all spin multiplets that comprise the Tl-205.203 NMR spectra and that arise from natural abundance Tl-205,Tl-203 and Se-77 or enriched Se-77 isotopomer distributions: The structures of all three anions are based on a Tl4Se4 cube in which Tl and Se atoms occupy alternate corners. There are one and two exo-selenium atoms bonded to thallium in Tl4Se54- and Tl4Se64-, respectively, so that these thalliums are four-cooridinate and possess a formal oxidation state of +3 and the remaining three-coordinate thallium atoms are in the +1 oxidation state. The structure of Tl5Se53- may be formally regarded as an adduct in which Tl+ is coordinated to the unique exo-selenium and to two seleniums in a cube face containing the Tl-III atom. The T4Se54-, Tl4Se64-, and Tl5Se53-anions and the presently unknown, but structurally related, Tl4Se44- anion can be described as electron-precise cages; Ab initio methods at the MP2 level of theory show that Tl4Se54-, Tl4Se64-, and Tl5Se53- exhibit true minima and display geometrical parameters that are in excellent agreement with their experimental cubanoid structures, and that Tl4Se44- is cube-shaped (T-d point symmetry). The gas-phase energetics associated with plausible routes to the formation and interconversions of these anions have been determined by ab initio methods and assessed. It is proposed that all three cubanoid anions are derived from the known Tl2Se22-, TlSe33-, Se-2(2-), and polyselenide anions that have been shown to be present in the solutions they are derived from.