Striking circular, labyrinthine, polygonal, and striped patterns of stones and soil self-organize in many polar and high alpine environments. These forms emerge because freeze-thaw cycles drive an interplay between two feedback mechanisms. First, formation of ice lenses in freezing soil sorts stones and soil by displacing soil toward soil-rich domains and stones toward stone-rich domains. Second, stones are transported along the axis of elongate stone domains, which are squeezed and confined as freezing soil domains expand. In a numerical model implementing these feedbacks, circles, labyrinths, and islands form when sorting dominates; polygonal networks form when stone domain squeezing and confinement dominate; and stripes form as hillslope gradient is increased.