<p>The discrete global grid system (DGGS), a multi-resolution hierarchical structure constructed by recursively dividing the Earth's surface, has promising applications in wide-area environmental modeling and geospatial computing. However, existing DGGS research faces several limitations. First, most DGGS implementations are restricted to a single grid-cell shape, such as triangular, rhombic, or hexagonal, which limits the flexibility to adapt grid structures to diverse application requirements. Second, current approaches predominantly focus on grid centers, neglecting the importance of vertices and edges (grid centers, vertices, and edges are collectively referred to as multi-structural elements). To address these challenges, this paper proposes a dual-structure approach to construct dual grid systems with multi-structural elements (DGSME) based on three regular polyhedra: the regular octahedron, icosahedron, and rhombic triacontahedron. DGSME supports hierarchical subdivision while preserving consistent orientation, thereby improving scalability and computational efficiency. The proposed framework enables the unique representation of multi-structural elements. As demonstrated in the case study, incorporating vertices and edges into the grid representation facilitates more detailed environmental modeling, yielding route planning outcomes with lower costs and reduced error compared to traditional single grid-centered models.</p>