A simple technique to construct high symmetry polyhedra and polytopes based on the Hückel method

This paper elaborates an application of the Hückel method, utilizing its inherent mathematical capacity to transform topological connectivity into geometric information for the construction of high symmetry polyhedra and polytopes. While traditionally used for electronic structure calculations, the method enables the geometrical reconstruction of structures through a specialized version of spectral embedding. The strong association of the Hückel method with the representation theory of symmetry groups provides a physical-grounded rationale for the procedure and a framework for interpretation of the results. The method extends seamlessly to higher-dimensional spaces and hierarchical structures. Making use of optimized, readily available software, it offers a practical and intuitive tool for structure generation in chemistry and condensed matter physics.