Author(s): Rui-Heng Liu and Xin Liu The authors introduce here a systematic and unified real-space recipe to build flat bands from symmetric compact localized states. Multiple examples across different lattice symmetries, orbital contents and dimensions validate the versatility of the scheme. In addition, the authors derive concise criteria for determining all topological band crossings in flat-band systems — including intriguing nodal type — and demonstrate their intimate connection to underlying symmetries. The findings provide a generic theoretical framework for studying flat band models and materials. [Phys. Rev. B 113, 035140] Published Wed Jan 21, 2026