Abstract In -duality-manifest formulations, supergravity fields are packaged into covariant objects such as the generalized metric and -form fields . While a parameterization of the generalized metric in terms of supergravity fields is known for -duality groups with , a parameterization of has not been fully determined. In this paper, we propose a systematic method to determine the parameterization of , which necessarily involves mixed-symmetry potentials. We also show how to systematically obtain the - and -duality transformation rules of the mixed-symmetry potentials entering the multiplet. As the simplest non-trivial application, we find the parameterization and the duality rules associated with the dual graviton. Additionally, we show that the 1-form field can be regarded as the generalized graviphoton in the exceptional spacetime.