Cp2M(dithiolene) (M = MoIV, WIV) d2 complexes exhibit a folding (theta) of the MS2C2 metallacycle along the S-S axis upon oxidation to the d1 paramagnetic cation. The evolution of the peculiar unfolded structure (theta = 0 degree) of Cp2Mo(dmit).+ (dmit2-, 2-thioxo-1,3-dithiole-4,5-dithiolate) in its AsF6- salt toward the introduction of heavy atoms (W, Se) is examined here by substituting dsit2- (dsit2-, 2-thioxo-1,3-dithiole-4,5-diselenolate) for dmit2- and/or W for Mo in those AsF6- salts. While [Cp2Mo(dsit).+][AsF6-] (orthorhombic, Cmcm, a = 9.071(2), b = 20.868(4), c = 10.243(2) A, V = 1938.9(7) A3, Z = 4) and [Cp2W(dmit).+][AsF6-] (orthorhombic, Cmcm, a = 9.0295(15), b = 20.568(2), c = 10.2641(12) A, V = 1906.2(4) A3, Z = 4) crystallize with an unfolded geometry and are isostructural with [Cp2Mo(dmit).+][AsF6-], the introduction of both W and dsit2- in Cp2W(dsit) stabilizes a fully different structure for [Cp2W(dsit).+][AsF6-] (monoclinic, P2(1)/c, a = 6.8442, b = 15.9923(13), c = 17.6594(16) A, beta = 90.934(11) degrees, V = 1932.6(3) A3, Z = 4) with the Cp2W(dsit).+ cation in a folded geometry (theta = 30.1(1) degrees). DFT calculations show that the variety of folding angles and hence of molecular structures found in those open-shell d1 Cp2M(dithiolene).+ complexes is attributable to a very low energy cost (< 1 kcal mol-1) for folding around the minimal energy folding angle. The molecular geometry of those complexes and hence their frontier orbitals are therefore highly related to the actual crystal structure they adopt. The unfolded complexes exhibit, in their AsF6- salts, a three-dimensional set of intermolecular interactions in the solid state, confirmed by the presence of an antiferromagnetic ground state (TNéel = 3.5(5) K in [Cp2W(dmit).+][AsF6-]). On the other hand, the folding of Cp2W(dsit).+ in [Cp2W(dsit).+][AsF6-] leads to the formation of a rare spin-ladder system with a spin gap of 90-100 K, as deduced from the temperature dependence of its magnetic susceptibility.