A 3D shape with all straight edges and flat faces is a polyhedron. Other 3D shapes with least one curved surface are not polyhedra. A 3D shape with regular polygonal faces, meeting at equal angles, is ...

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 ...

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 ...

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 ...