  Ribbons are topological objects of biological and technological importance.
Here, we study the folding of thick ribbons with hydrophobic surfaces in a bad
solvent in regimes in which either the ribbon's thickness or the solvent
molecule size is not vanishingly small compared to the ribbon's width.
Extensive Monte Carlo simulations show that ribbons of various lengths and with
a small stiffness adopt several distinct configurations as the ground state
that include rolled (Archimedean spiral), curled, twisted and globule
conformations. Analytic and numerical calculations based on the consideration
of putative ground states lead to phase diagrams that qualitatively agree with
the simulation results. A symmetry breaking of the planar rolled configuration
in favor of the elongated twisted and the globular ribbons is observed on
increasing the solvent size. Interestingly, the twisted ribbon is found as the
ground state in the absence of any energetic preference for twisting. We show
that the twist of the DNA double helix structure can be stabilized when modeled
as a hydrophobic thick ribbon even in the limit of vanishing solvent size.
