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Space deformations or free-form deformations techniques are a powerful tool to manipulate and to animate objects. Various extensions of these techniques allow a user to intuitively deform objects, but none of these propose a solution to preserve the volume of objects throughout the deformation. This paper introduces a new method to deform an object, its volume being preserved. Our method is based on the space deformation model called DOGME. We use a distinctive feature of DOGME to solve the problem of volume preservation. Polyhedral objects which are currently used in geometric modeling are considered and we obtain excellent results in a fully intuitive and interactive environment.