A **Heronian tetrahedron** is a tetrahedron whose side lengths, face areas and volume are all rational numbers. The faces must therefore all be Heronian triangles.

A regular tetrahedron with rational sides is not a Heronian tetrahedron because its face areas and volume are not rational numbers. A Heronian tetrahedron is sometimes called a **perfect tetrahedron**.

117 is the smallest possible length of the longest side of a perfect tetrahedron. Its other sidelengths are 51, 52, 53, 80 and 84.

## See also

## External links

This polyhedron-related article is a stub. You can help Math Wiki by expanding it. |