  Explicit solutions to the Riemann-Hilbert problem will be found realising
some irreducible non-rigid local systems. The relation to isomonodromy and the
sixth Painleve equation will be described.
  Keywords: Riemann-Hilbert problem, Painleve equations, algebraic solutions,
Heun equations, tetrahedral/octahedral group, triangle groups, Belyi maps.
