The Triassic salt in Cheshire, England, has large polygonal patterns on bedding surfaces. The polygons are bounded by deep V-shaped fissures. The fissures have a banded internal structure made up of individual units of pure secondary salt and clastic-rich halite. The salt was deposited from shallow brines in an arid environment. A thermal contraction model is proposed here for the formation of the polygons. Calculations of the depth of penetration of thermal waves and the net contraction of salt beds indicate that annual temperature fluctuations would produce fissures of the observed depth and width. It is suggested that thermal contraction is the most important factor in the initiation of all polygonal patterns on salt surfaces and that the polygon form that eventually develops is dependent on the thickness of the salt bed and the availability of brines to the salt surface.