The Bernstein–Gelfand–Gelfand (BGG) framework provides a systematic approach for deriving new complexes from well-understood ones, such as the de Rham complex. In this work, we introduce a discrete BGG diagram and its associated complexes in two dimensions, defined from discrete Stokes and de Rham complexes using polytopal methods. While this construction has previously been developed in the context of finite elements, this work presents the first formulation based on polytopal methods. The polytopal approach removes certain constraints inherent to finite elements, can lead to lighter computational methods, and allows the use of more flexible meshes. Such flexibility is particularly useful for capturing domain singularities or handling complex geometries. This construction has applications to plate models, including the Reissner–Mindlin and Kirchhoff–Love models. This is joint work with Daniele Di Pietro, Jérôme Droniou, and Kaibo Hu.