This paper introduces ComFormer, a novel SE(3) transformer for crystal property prediction, which utilizes geometrically complete crystal graphs to capture the complete geometric information of crystals. The proposed method addresses the challenges of representing periodic and infinite crystal structures, including handling chiral crystals and maintaining geometric completeness. ComFormer includes two variants: iComFormer, which employs invariant geometric descriptors, and eComFormer, which uses equivariant vector representations. The method is evaluated on three widely-used crystal benchmarks, demonstrating state-of-the-art predictive accuracy across various tasks. The proposed crystal graphs and ComFormer variants are geometrically complete, ensuring that different crystal structures are uniquely represented. The method is efficient, with a complexity of O(nk), where n is the number of atoms in the unit cell and k is the average number of neighbors. The results show that ComFormer outperforms existing methods in predicting crystal properties, highlighting the effectiveness of the proposed geometrically complete crystal graphs and the ComFormer architecture. The code is publicly available as part of the AIRS library.This paper introduces ComFormer, a novel SE(3) transformer for crystal property prediction, which utilizes geometrically complete crystal graphs to capture the complete geometric information of crystals. The proposed method addresses the challenges of representing periodic and infinite crystal structures, including handling chiral crystals and maintaining geometric completeness. ComFormer includes two variants: iComFormer, which employs invariant geometric descriptors, and eComFormer, which uses equivariant vector representations. The method is evaluated on three widely-used crystal benchmarks, demonstrating state-of-the-art predictive accuracy across various tasks. The proposed crystal graphs and ComFormer variants are geometrically complete, ensuring that different crystal structures are uniquely represented. The method is efficient, with a complexity of O(nk), where n is the number of atoms in the unit cell and k is the average number of neighbors. The results show that ComFormer outperforms existing methods in predicting crystal properties, highlighting the effectiveness of the proposed geometrically complete crystal graphs and the ComFormer architecture. The code is publicly available as part of the AIRS library.