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Heronian tetrahedron

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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.

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