A toy construction kit has a plurality of magnetic modules, each with a housing having a plurality of sides, each side having an internal hollow. A magnet is contained within each of the hollows at a given polar orientation relative to the housing and the hollow. The hollow has dimensions that permit the magnet to move within the hollow, but substantially constrains the magnet to the given polar orientation relative to the housing. When a side of a module is placed near a side of another module, they are bound by magnetic attraction by the respective aligned magnets, either because the polar orientations are opposite when they are initially juxtaposed or due to shifting of one or both magnets in their respective hollows to achieve relative polar opposition.