Heronian tetrahedron

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

A regular tetrahedron (one with all faces being equilateral) with all sides rational is not a Heronian tetrahedron because its face areas and volume are not rational numbers.

117 is the smallest possible length of the longest edge of a perfect tetrahedron with integral edge lengths. Its other edge lengths are 51, 52, 53, 80 and 84.

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