In this paper we introduce the concept of a Reconfigurable Tangible Device for manipulation of 3D objects in virtual environments by single or multiple users. This Reconfigurable Tangible Device (RTD) provides points of manipulation rigidly linked together. The shape of the RTD can be reconfigured at any time as its arms can be compressed or stretched by users at will. Due to its simple shape the Reconfigurable Tangible Device can be attached to any 3D virtual object. Then, it can fully define the motion of the virtual object in 6 Degrees of Freedom. Two examples of Reconfigurable Tangible Device were developed: one with three points of manipulation (a reconfigurable triangle) and one with four points. We illustrate how these two simple devices can match many different shapes of 3D objects, and in different contexts. Preliminary testing was conducted with the RTD based on three points of manipulation involving a collaborative manipulation task in virtual reality. It produced better subjective appreciation for the RTD compared to more classical 3D collaborative techniques.