Tropical Lines on Cubic Surfaces

Given a tropical line $L$ and smooth surface $X$, we look at the position of on $X$. We introduce its primal dual motifs which are respectively decorated graph subcomplex triangulation They encode combinatorial classify all possible lines general surfaces. This classification allows us to give an upper bound for number with given subdivision. focus in particular surfaces degree three. As concrete example, cubic fixed honeycomb triangulation, showing that contains exactly $27$ lines.