The crystal structures of three thermal polymorphs (I, II, and III) for each isomer of closo-dicarbadodecaboranes C2B10H12 (ortho, meta, and para) have been determined by combining synchrotron radiation X-ray powder diffraction and density functional theory calculations. The structures are in agreement with previous calorimetric and spectroscopic studies. The difference between rotatory phases (plastic crystals) I and II lies in isotropic rotations in the former and anisotropic rotations of the icosahedral clusters in the latter. Phase I is the cubic close packing (ccp) of rotating closo-molecules C2B10H12 in the space group Fm3̅. Phase II is the ccp of rotating closo-molecules C2B10H12 in the cubic space group Pa3̅. The preferred rotational axis in II varies with the isomer. The ordered phases III are orthorhombic (meta) or monoclinic (ortho and para) deformations of the cubic unit cell of the disordered phases I and II. The ordering in the phase III of the ortho-isomer carrying the biggest electrical dipole moment creates a twofold superstructure w.r.t. the cubic unit cell. The thermal polymorphism for C2B10H12 and related metal salts can be explained by division of the cohesive intercluster interactions into two categories (i) dispersive cohesive interaction with additional Coulombic components in the metal salts and (ii) anisotropic local interaction resulting from nonuniform charge distribution around icosahedral clusters. The local interactions are averaged out by thermally activated cluster dynamics (rotations and rotational jumps) which effectively increase the symmetry of the cluster. The C2B10H12 molecules resist at least as well as the CB11H12- anion to the oxidation, and both clusters form easily a mixed compound. This allows designing solid electrolytes such as Nax(CB11H12)x(C2B10H12)1-x, where the cation content may be varied and the temperature of transition into the disordered conducting phase is decreased.