Current research on three-dimensional metamaterial has largely focused on conventional strut, plate, and shell-based lattice designs. Although these designs offer several advantages, they possess inherent limitations that can restrict their performance in certain applications, motivating the exploration of alternative structural topologies. Here, we present a large-scale, symmetry guided framework for the generation and analysis of architected metamaterials based on all 36 cubic space groups. Using a voxel-based representation, we construct a database of approximately 1.95 million periodic unit cells spanning a broad range of relative densities and topological complexity. This dataset reveals a rich elastic property landscape shaped by crystallographic symmetry, including rare pentamode designs with high bulk to shear ratios such as $K/G \approx 166$ , isotropic-auxetic architectures with Poisson's ratio as low as $ν=-0.76$, and structures achieving up to 93% of the Hashin-Shtrikman upper bound on stiffness. Complementing the dataset, we develop a three-dimensional convolutional neural network surrogate model trained and evaluated on the full database to predict strain-energy density values under uniaxial, shear, and hydrostatic loading. Together, this work establishes a comprehensive atlas of cubic symmetric metamaterials and provides a pre-trained model for the accelerated discovery and design of 3D architected materials with extreme mechanical properties.

翻译：当前三维超材料的研究主要集中于传统的杆状、板状和壳状晶格设计。尽管这些设计具有诸多优势，但其固有的局限性可能限制其在某些应用中的性能，这促使人们探索替代的结构拓扑。本文提出了一种基于全部36种立方空间群的大规模对称性引导框架，用于结构超材料的生成与分析。采用体素表示法，我们构建了包含约195万个周期性单胞的数据库，涵盖了广泛的相对密度和拓扑复杂度范围。该数据集揭示了由晶体学对称性塑造的丰富弹性性能图谱，包括具有高体剪切比（如$K/G \approx 166$）的罕见五模设计、泊松比低至$ν=-0.76$的各向同性拉胀结构，以及刚度达到Hashin-Shtrikman上界93%的结构。作为数据集的补充，我们开发了一个三维卷积神经网络代理模型，该模型在全数据库上进行训练和评估，用于预测单轴、剪切和静水载荷下的应变能密度值。本工作共同构建了立方对称超材料的综合图谱，并为加速发现和设计具有极端力学性能的三维结构材料提供了预训练模型。