How to import mixed triangle and quad meshes from gmsh to fenics

Your guess is as good as mine. The only things required to create a mesh in dolfin is:

  1. The points of the mesh (msh.points)
  2. The connectivity if each cell (msh.cells)
  3. The physical data tags (msh.cell_data)

See for instance: Transitioning from mesh.xml to mesh.xdmf, from dolfin-convert to meshio