Duke's realization conjecture for triangulated tori

A triangulated torus is a simplicial triangulation of the topological $2$-torus, and a polyhedral realization in $\mathbb{R}^3$ is a geometric realization as a polyhedral surface.

Duke's torus-realization conjecture. Every triangulated torus can be realized as a polyhedron in $\mathbb{R}^3$.

The question concerns geometric realizability of triangulated orientable surfaces. The source states that realizability of the $2$-torus was still open and attributes this conjecture to Duke.