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Multi-layer spatial structures usually take considerable external loads with very limited material usage at all scales, and Polyhedral Graphic Statics (PGS) provides a method to design multi-layer funicular polyhedral structures. The structural forms usually materialized as space frames. Our previous research shows that the intrinsic planarity of the polyhedral geometries can be harnessed for efficient fabrication and construction processes using flat-sheet materials. Sheet-based structures are advantageous over the conventional space frame systems because sheets can provide more load paths and constrain the kinematic degrees of freedom of the nodes. Therefore, they can take a wider range of load compared to space frames. Moreover, sheet materials can be fabricated to complex shapes using CNC milling, laser cutting, water jet cutting, and CNC bending techniques. However, not all sheets are necessary as long as the load paths are preserved, and the system does not have kinematic degrees of freedom. To find a reduced set of faces that satisfies the requirements, this paper incorporates and adapts the matrix analysis method to calculate the kinematic degree of freedom of sheet-based structure. Built upon this, an iterative algorithm is devised to help find the reduced set of faces with zero kinematic degree of freedom. To attest the advantage of this method over bar-node construction, a comparative study is carried out using finite element analysis. The result shows that, with the same material usage, the sheet-based system has improved performance than the framework system under a wide range of loading scenarios.