Volume of Smallest Tetrahedron with Integer Edges and Integer Volume
Theorem
The volume of the smallest tetrahedron with integer edges and integer volume is $3$.
There are $2$ possible sets of edges:
- $32, 33, 35, 40, 70, 76$
- $21, 32, 47, 56, 58, 76$
Proof
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Sources
- Apr. 1992: Kevin L. Dove and John S. Sumner: Tetrahedra with Integer Edges and Integer Volume (Math. Mag. Vol. 65, no. 2: 104 – 111) www.jstor.org/stable/2690489
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $3$
