A tip for a turbine component, turbine rotor blade or tip of a blade, is disclosed. The tip includes a tip plate configured to be coupled at a tip end of an airfoil chamber; and a tip rail extending radially from the tip plate, the tip rail disposed near or at a periphery of the tip plate. The trip rail includes a cooling structure constituting at least a portion of the tip rail. The cooling structure is in fluid communication with the airfoil chamber, and includes a plurality of repeating, three dimensional unit cells. Each unit cell defines a flow passage that is in fluid communication with the flow passage of at least one other unit cell. The flow passages of the 3D unit cells create a tortuous cooling passage in at least a portion of the tip rail.