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
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Sources
- 1992: R.H. Buchholz: Perfect Pyramids (Bull. Austral. Math. Soc. Vol. 45: pp. 353 – 368)
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $18,144$
- Weisstein, Eric W. "Heronian Tetrahedron." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/HeronianTetrahedron.html