The works of the Greek polymath Plato have kept people busy for millennia. Mathematicians have long pondered Platonic solids, a collection of geometric forms that are highly regular and are frequently ...

Consider what happens when a vertex of one tetrahedron pierces the face of a second tetrahedron to form a new, more complicated polyhedron. In the resulting geometric form, one triangular face has a ...

Taking published crystal structures of metal oxides as examples, we demonstrate below that ellipsoidal analysis based on fitting the MBE provides new insights into phase transitions in perovskites, ...