We present PuppetX, a framework for both constructing playthings and playing with them using spatial body and hand gestures. This framework allows users to construct various playthings similar to puppets with modular components representing basic geometric shapes. It is topologically-aware, i.e. depending on its configuration; PuppetX automatically determines its own topological construct. Once the plaything is made the users can interact with them naturally via body and hand gestures as detected by depth-sensing cameras. This gives users the freedom to create playthings using our components and the ability to control them using full body interactions. Our framework creates affordances for a new variety of gestural interactions with physically constructed objects. As its by-product, a virtual 3D model is created, which can be animated as a proxy to the physical construct. Our algorithms can recognize hand and body gestures in various configurations of the playthings. Through our work, we push the boundaries of interaction with user-constructed objects using large gestures involving the whole body or fine gestures involving the fingers. We discuss the results of a study to understand how users interact with the playthings and conclude with a demonstration of the abilities of gestural interactions with PuppetX by exploring a variety of interaction scenarios.