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, ...

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 ...

Advances in fabrication technologies are enabling the production of architected materials with unprecedented properties. Most such materials are characterized by a fixed geometry, but in the design of ...

For most people, the word “polyhedron” conjures up an image of a cube, a tetrahedron, or something similar—a solid figure with flat faces. If the polyhedron is regular, each face has the same size and ...

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 ...

Royal Society Research Fellow and Senior Birmingham Fellow, University of Birmingham The work of the Greek polymath Plato has kept millions of people busy for millennia. A few among them have been ...