In point cloud classification, point-based methods have drawn significant attention in recent years. Prior work typically focuses on finding relationships between points or vectors to extract low-order features for classification tasks. However, these low-order features cannot fully represent the 3D objects. To address this limitation, we propose a novel plug-and-play PointSC block that uses simplicial complex analysis to explore topological structures and extract both algebraic and geometric features across multiple dimensions, including 0-simplex (point), 1-simplex (line), and 2-simplex (triangle). For each type of simplex, we define the simplex grouping, algebraic feature representation, and geometric representation to construct and extract topological information from the point cloud. Our experimental results demonstrate that our PointSC network achieves state-of-the-art performance and computational efficiency on the ModelNet40 and ScanObjectNN datasets.