This paper considers a set of nodes exchanging data at fair rates with the help of a relay. It is called generalized bidirectional relaying, since it is valid for any number of nodes. The relaying protocol, composed of alternate MAC phases, where only two nodes transmit to the relay, and broadcast phases, where the relay transmits to all nodes, is detailed. The maximum achievable data rates are then analytically determined, under the constraint that all links should communicate at the same rate, and under a sum power constraint. Two physical layer relaying strategies are studied, and compared with the cut-set upper bound: lattice-based coding and Decode-and-Forward. The fair data rate achievable with lattice-based coding asymptotically converges to the cut-set upper-bound, whereas Decode-and-Forward asymptotically tends to half of these values.