A wheel apparatus includes a hub that is configured to be received by an axle of an irrigation system. The wheel apparatus also includes a rim assembly that includes a plurality of substantially flat feet that form a faceted circular arrangement. A support structure is disposed between the hub and the rim assembly to at least partially support the rim assembly. At least one of the substantially flat feet is coupled to at least one of the plurality of spoke structures. The wheel apparatus also includes at least one cleat disposed on an outside surface of at least one of the plurality of substantially flat feet to provide traction to the rim assembly.