A set of positive integers $d_1, \dots, d_n$ describe two n-dimensional closed lattice tetrahedron: $$ T = \left\{ (x_1, \dots, x_n) \in \mathbb{R}^n: \sum_{i=1}^n \frac{x_i}{d_i} \leq 1 \textrm{ and all } x_i \geq 0 \right\}.$$ Let $L_T(t)$ be the Ehrhart polynomial of $T$, i.e. the number of integer lattice points in $tT$.

When are all coefficients of $L_{T}(t)$ positive?