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 distinctive three-dimensional shape in Albrecht Dürer’s 1514 engraving Melencolia I has been the subject of innumerous analyses and still no one is sure what it is or what it means. On the ...

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 ...