Patterned self-assembled monolayers (SAMs) of alkanethiolates on gold films were used as constraining elements in forming shapes, in a strategy based on minimizing interfacial free energy. Circular right cylinders, catenoids, and other related shapes having centimeter dimensions were formed from poly(dimethylsiloxane) (PDMS) in a system comprising patterned SAMs and an aqueous solution of sodium chloride whose density equaled that of the polymer. These shapes were fabricated without using complementary, three-dimensional molds: the final form adopted by the PDMS was a minimum free energy shape with certain features of the shape set by the wetting of the pattern in the SAM by the PDMS. Using previously formed polymeric shapes and patterned SAMs as constraining elements, a cylinder fused with a catenoid, a cylinder fused with a truncated cone, two truncated cones fused together, and a truncated cone fused with a hemisphere were fabricated. Applying a magnetic field gradient influenced the final shape of the polymer by generating an effective spatial gradient in the density of the solution. Without using SAMs as constraining elements, convex-concave and double convex lenses were formed at interfaces of two immiscible liquids. Shapes with micrometer dimensions were fabricated by microcontact printing of patterned SAMs and self-assembly of a polymer on these patterns. These procedures produced shapes such as arrays of channel waveguides (with width of a few micrometers) and microlenses (with diameter of 1-2 mu m).