Volume of Smallest Rational Tetrahedron

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Theorem

The only rational tetrahedron whose edge lengths are less than $157$ has:

edges of length $117$, $80$, $53$, $52$, $51$, $84$
faces of area $1800$, $1890$, $2016$, $1170$
volume of $18 \, 144$.


Proof


Sources