The software Cabri 3D allows the nets of polyhedra to be constructed using one or more sets of connected polygons where the angle between all connected polygons is the same. These collections can be folded into the polyhedron by dragging a point controlling the angle between the polygons. Viewed from above, the polygons act as a kaleidoscope as the angle changes, and when the angle is decreased so that polygons intersect, surprisingly beautiful symmetric figures emerge, which can be constructed as physical artifacts or experienced as dynamic computer animations.