Receive emails about upcoming NOVA programs and related content, as well as featured reporting about current events through a science lens. Let me explain, first, what the Platonic solids are. To ...

Named for Plato, who theorized that the classical elements were made of these regular polyhedrons, three of the Platonic solids are composed of equilateral triangles: the tetrahedron, octahedron, and ...

Some definitions are in order here. A lattice Λ in is an infinite set of points generated by a set of discrete translation operations (defined by integer linear combinations of a basis of ) (ref. 4).

The highlight of the 13th and final book of Euclid's Elements was the proof that there are just five "Platonic solids". Recall that a regular polygon is a plane figure with all sides and angles equal, ...