A contact lens has a core thick enough to accommodate a payload. The lens further has outer and inner coverings that cover parts of the core. Each covering is a thin layer of gas-permeable material shaped to form a respective cavity between the covering and the core. Oxygen passes through the outer covering to the outer cavity, through an air path within the core to the inner cavity, and through the inner covering to reach the cornea of the wearer's eye. To increase oxygen flow, a patterned structure is formed at an interface between the core and at least one of the outer and inner covering, comprising supports at which the core and covering contact, and recesses forming the cavity between the core and covering for oxygen flow. Because each recess spans only a short distance between supports, portions of the covering may be made thinner to improve oxygen flow.