Flat band (FB) systems provide ideal playgrounds for studying correlated physics, whereas multi-orbital characteristics in real materials are distinguished from most simple FB models. Here, we propose a systematic and versatile symmetry-based framework for FB constructions in tight-binding (TB) models based on symmetric compact localized states (CLSs), integrating lattice and orbital degrees of freedom. The essential perspective is to capture destructive interference, which is universal for FBs, by reinterpreting the Hamiltonian as a linear mapping and searching for symmetric CLSs in the kernel. To illustrate the versatility of our framework, we construct three representative FB models: one in two dimensions (2D) and the rest in three dimensions (3D). All of them lack special lattice structures and incorporate high orbitals. Further, we unveil 3D FBs exhibiting exotic nodal-line band touchings. For a comprehensive understanding, we derive a concise criterion for determining all band touchings and demonstrate their symmetry-protected nature. Our work offers a systematic approach to construct FBs across diverse lattice systems and opens new avenues for understanding and engineering FB systems, with potential implications for correlated quantum phenomena and exotic phases of matter.

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• Flat bands
• 2-dimensional systems
• 3-dimensional systems
• Bloch wave theory
• Lattice models in condensed matter