This paper addresses the challenge of representing and predicting properties of crystal materials using graph neural networks. The authors introduce a novel approach that leverages the periodic patterns of unit cells to establish lattice-based representations for each atom, enabling efficient and expressive graph representations of crystals. They propose ComFormer, a SE(3) transformer designed specifically for crystalline materials, which includes two variants: iComFormer, which uses invariant geometric descriptors of Euclidean distances and angles, and eComFormer, which employs equivariant vector representations. Experimental results on three widely-used crystal benchmarks demonstrate the state-of-the-art predictive accuracy of ComFormer variants on various tasks. The code for the proposed methods is publicly available as part of the AIRS library. The paper also discusses the importance of geometric completeness in crystal graph representations and provides detailed proofs of the proposed methods' effectiveness.This paper addresses the challenge of representing and predicting properties of crystal materials using graph neural networks. The authors introduce a novel approach that leverages the periodic patterns of unit cells to establish lattice-based representations for each atom, enabling efficient and expressive graph representations of crystals. They propose ComFormer, a SE(3) transformer designed specifically for crystalline materials, which includes two variants: iComFormer, which uses invariant geometric descriptors of Euclidean distances and angles, and eComFormer, which employs equivariant vector representations. Experimental results on three widely-used crystal benchmarks demonstrate the state-of-the-art predictive accuracy of ComFormer variants on various tasks. The code for the proposed methods is publicly available as part of the AIRS library. The paper also discusses the importance of geometric completeness in crystal graph representations and provides detailed proofs of the proposed methods' effectiveness.