A gallery of pullback maps

This is a hand-picked collection of pullback map drawings taken from the Hurwitz classes menu. They were chosen so that

  1. deg(f) ≤ 9,
  2. they are essentially different and
  3. the group of all symmetries of the pullback map acts on the upper half-plane as a reflection group.
This latter condition makes it very likely that the drawing is correct. It seems to always be possible to verify that a drawing is correct by (verifying and) using the information in the Hurwitz classes menu.