In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons) is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the ordinary convex polyhedra and the only one that has fewer than 5 faces.

The tetrahedron is the three-dimensional case of the more general concept of a Euclidean simplex.

The tetrahedron is one kind of pyramid, which is a polyhedron with a flat polygon base and triangular faces connecting the base to a common point. In the case of a tetrahedron the base is a triangle (any of the four faces can be considered the base), so a tetrahedron is also known as a "triangular pyramid".

Like all convex polyhedra, a tetrahedron can be folded from a single sheet of paper. It has two such nets.

For any tetrahedron there exists a sphere (called the circumsphere) on which all four vertices lie, and another sphere (the insphere) tangent to the tetrahedron's faces.

Regular tetrahedron

A regular tetrahedron is one in which all four faces are equilateral triangles. It is one of the five regular Platonic solids, which have been known since antiquity.

Tetrahedron is a weekly peer-reviewed scientific journal covering the field of organic chemistry. According to the Journal Citation Reports, the journal has a 2014 impact factor of 2.641.Tetrahedron and Elsevier, its publisher, support an annual symposium.

Notable papers

As of 22 June 2013, the Web of Science lists ten papers from Tetrahedron that have more than 1000 citations. The four articles that have been cited more than 2000 times are: