In this paper, we enumerate the parameter matrices of all perfect $2$-colorings of the Platonic graphs consisting of the tetrahedral graph, the cubical graph, the octahedral graph, the dodecahedral graph, and  the icosahedral graph.

The Wigner-Racah algebra of an arbitrary (finite or compact continuous) group is presented in an original way that constitutes a straightforward extension of the corresponding algebra of the rotation group. Illustrative examples are given around the rotation group and the octahedral group. The adaptation of the Wigner-Racah algebra of the double rotation group to one of its subgroups G is discu...

Formation of tetrahedral or octahedral condensation related to the experiments on electrolysis or deuterium permeation was studied. We obtained the scenario about the formation that alkali or alkaline-earth metal ions infiltrating into the host metal made cavities there when they hopped onto the other sites of the crystal lattice of it, then through squeezing of H/D ions in the cavity tetrahedr...

The distribution of Ga and A1 atoms within the octahedral sheets of synthetic goethites has been investigated by XRD and Ga K-edge XANES and EXAFS spectroscopies. XRD results indic te a solid solution between goethite (aFeOOH) and GaGoe4 (40 mol% of Ga). The XANES data indicate the presence of &a in the solid solution. The fitting procedures for EXAFS spectra show no evidence of preferential oc...

For ABO3 perovskites, octahedral rotations and distortions couple strongly to the functional properties. However, in short period perovskite superlattices, the characterization of the octahedral behavior remains challenging due to the local structural variations of the BO6 octahedra. By aberration-corrected high-resolution transmission electron microscopy, we investigated the local octahedral r...