4-dimensional polytopes can be visualized by projecting them to our 3-space. The projections are usually represented either with computer-generated animations or with rigid objects. This paper deals with the possibility of representing a polychoron with a kinetic 3-dimensional model. A stereographic projection of the 16-cell is constructed with six hexagram links of wire forming Chinese crosses at the eight vertices. The symmetry of the model permits a manipulation similar to the ‘hyper-rotation’ in animations representing stereographic projections of polychora. Playing with the design offers a hands-on approach to the study of 4-dimensional geometry and the hypersphere.