Describing 4-stars at 5-vertices in normal plane maps with minimum degree 5

We refine the tightness of Borodin-Woodall's bound 30 by presenting six M5s such that (1) every 4-star at a 5-vertex in them has weight at least 30 and (2) for each of the six possible types (5,5,5,10), (5,5,6,9), (5,5,7,8), (5,6,6,8), (5,6,7,7), and (6,6,6,7) of 4-stars with weight 30, the 4-stars of this type at 5-vertices appear in precisely one of these six M5s.