It is well known that two regular tetrahedra can be combined with a single regular octahedron to tile (complete fill) three-dimensional Euclidean space . This structure was called the "octet truss" by Buckminster Fuller. It was believed that such a tiling, which is the Delaunay tessellation of the face-centered cubic (fcc) lattice, and its closely related stacking variants, are the only tessell...

The syntheses, structures, and magnetic properties are reported for three new Ce/Mn clusters with different Ce/Mn ratios: [Ce6Mn4O12(O2CMe)10(NO3)4(py)4] (py = pyridine) (1), [CeMn8O8(O2CCH2(t)Bu)12(DMF)14] (DMF = dimethylformamide) (2), and [Ce2Mn4O2(O2CMe)6(NO3)4(hmp)4] (3; hmp(-) is the anion of 2-(hydroxymethyl)pyridine). 1 and 2 were obtained from the reaction of Ce(IV) with [Mn12O12(O2CMe...

Organic ligand-protected metal nanoclusters have attracted extensively attention owing to their atomically precise composition, determined atom-packing structure and the fascinating properties and promising applications. To date, most research has been focused on thiol-stabilized gold and silver nanoclusters and their single crystal structures. Here the single crystal copper nanocluster species...

Large ('1000 atoms) supercell valence force-field simulations are used to investigate the nearest-neighbor bond-length distribution in relaxed tetrahedral ~zinc blende and wurtzite! and octahedral ~rocksalt! Ga12xInxN alloys. We find that, due to the rigidity of the octahedron, the distribution of each anion-cation bond length in rocksalt alloys has two contributions: unrelaxed bonds and relaxe...

Abstract The notion of strong electronic correlations arose in the context d -metal oxides such as NiO but can be exemplified on systems simple H 2 molecule. Here we shed light correlation effects B 6 2− clusters found M hexaborides and show that p valence electrons are fairly correlated. -octahedron excitation energies computed for CaB YbB agree with peak positions by resonant inelastic x-ray ...

In a previous article, we have proposed that the large scale structure network generated by large scale magnetic fields could consist of a network of octahedra only contacting at their vertexes. Assuming such a network could arise at different scales producing a fractal geometry, we study here its properties, and in particular how a sub-octahedron network can be inserted within an octahedron of...

We prove that any simple polytope (and some non-simple polytopes) in R admits an inscribed regular octahedron.

The paper "Unified Field Theory and the Configuration of Particles" opened a new chapter of physics. One of the predictions of the paper is that a proton has an octahedron shape. As Physics progresses, it focuses more on invisible particles and the unreachable grand universe as visible matter is studied theoretically and experimentally. The shape of invisible proton has great impact on the topo...