A construction kit that is suitable for creating a variety of different structures includes a plurality of illuminated elements. In one embodiment, an illuminated element has a plurality of substantially transparent panels forming a three-dimensional shape, a self-powered light cartridge within the three-dimensional shape, and a plurality of externally directed magnets. The cartridge can include a housing disposed on a panel of the plurality of substantially transparent panels, a light located within the housing and positioned approximately in the center of the three-dimensional shape, circuitry within the housing for controlling an operation of the light, a battery within the housing for powering the light via the circuitry, and a removable cover for sealing the light, circuitry and battery within the housing. The illuminated elements can be directly connected to each other with the externally directed magnets or with connecting members (e.g., ferromagnetic spheres) between the magnets.