On Lattice Barycentric Tetrahedra
Brian Mazur
Abstract
We say a lattice tetrahedron whose centroid is its only non-vertex lattice point is lattice barycentric. The notation T(a,b,c) describes the lattice tetrahedron with vertices 0, e1, e2, a e1 + b e2 + c e3. Our result is that all such T(a,b,c) are unimodularly equivalent to T(3,3,4) or T(7,11,20).
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