Polarized light mosaics (PLMs) are color-changing structures that alter their appearance based on the orientation of incident polarized light. While a few artists have developed techniques for crafting PLMs by hand, the underlying material properties are difficult to reason about; there exist no tools to bridge the high-level design objectives with the low-level physics knowledge needed to create PLMs. In this paper, we introduce the first system for creating Polagons: machine-made PLMs crafted from cellophane with user-defined color changing behaviors. Our system includes an interface for designing and visualizing Polagons as well as a fabrication process based on laser cutting and welding that requires minimal assembly by the user. We define the design space for Polagons and demonstrate how formalizing the process for creating PLMs can enable new applications in fields such as education, data visualization, and fashion.