This paper proposes a novel deployable hexahedron mobile mechanism that is rigidly linked by only prismatic joints. The mechanism that is a completely symmetrical structure can always keep the walking capability when any of its six faces of the hexahedron touches the ground. It can roll at any stable state. The configuration constructed by only prismatic joints makes it expand and contract as a deployable structure. In this paper, a method for constructing a deployable hexahedron mobile mechanism is proposed. The stability analysis and dynamic simulation of the walking and rolling are carried out. The necessary condition of tipping motion and the speed analysis of two different rolling gaits are studied in details. A binary control strategy is adopted to simplify the complexity of the control system. A pneumatic cylinder is chosen to be the binary actuator. A prototype composed of 180 pneumatic cylinders was fabricated. The validity of the walking and tipping functions are verified by the experimental results.