This dissertation investigates the design of sheet-based structures using polyhedral graphic statics (PGS). It aims to address the practical limitations of PGS as a structural form-finding tool, focusing on both the equilibrium and stability of polyhedral funicular structures. For the equilibrium aspect, an enhanced algebraic formulation for PGS and its computational implementation is presented, which surpasses existing implementations in precision and efficiency. This development is the foundation for the form-finding explorations throughout the dissertation and is useful for all PGS-related research and applications beyond this work. For the stability aspect, a method for evaluating the kinematic indeterminacy of pin-jointed and face-hinge assemblies, adapted from the matrix analysis of pin-jointed frameworks, is introduced. This method can quickly evaluate the displacement state associated with a specific load case using minimal inputs, making it a handy tool for stability simulation and form-finding in early-stage structural designs. Three concepts of sheet-based construction are progressively explored to ensure structural efficiency and stability. First, a method that materializes all planar faces as sheet materials is demonstrated through a 3-meter-span glass bridge, showcasing the stability and ease of construction of such designs. The second concept involves removing some faces without compromising stability, which identified an issue with sheet buckling. To address this, the third concept proposes using curved sheets combined with force diagram subdivision, which unifies considerations for both equilibrium and stability. All concepts are designed to be compatible with planar sheet materials and existing fabrication techniques.