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 ...

Four mathematicians have cataloged all the tetrahedra with rational angles, resolving a question about basic geometric shapes using techniques from number theory. The tetrahedron is the simplest three ...

A four-sided shape that will always come to rest on the same side no matter what side it starts on has been built by mathematicians, decades after it was first proposed to exist. Mathematicians have ...