In the paper Motivic Lefschetz Theorem for twisted Milnor Hypersurfaces, we associate a graph to a hyperplane section in a twisted Milnor hypersurface according to its toric fixed points and toric stable curves. When $n=5$, there are $20$ vertices which can be distributed as vertices of a regular dodecahedron. Two types of edges then form two families (compounds) of 5 tetrahedra. We constructed $5$ classes each of which is supported over a single tetrahedron on the left diagram, and the monodromy action is given by rotations.
The diagrams are generated by SageMath.