An intermediate connector is provided for coupling to a set of illuminating modules. The intermediate connector has a set of connector arms, wherein each arm has an end that projects over a length from a body of the intermediate connector; a shape to fit into an opening of a corresponding illuminating module to provide, when the arm is seated in the illuminating module, both an electrical connection and a mechanical connection to the corresponding illuminating module; and an external wall with a taper along the length, wherein the end has a cross sectional area, including an areal quantity attributable to thickness of the external wall, that is smaller than a cross sectional area of the opening of the corresponding illuminating module.