Architected materials are materials engineered to utilize their topological aspects to enhance the related physical and mechanical properties. With the witnessed progressive advancements in fabrication techniques, obstacles and challenges experienced in manufacturing geometrically complex architected materials are mitigated. Different strut-based architected lattice structures have been investigated for their topology-property relationship. However, the focus on lattice design has recently shifted toward structures with mathematically defined architectures. In this work, we investigate the architecture-property relationship associated with the possible configurations of employing the mathematically attained Schoen's I-WP (IWP) minimal surface to create lattice structures. Results of mechanical testing showed that sheet-based IWP lattice structures exhibit a stretching-dominated behavior with the highest structural efficiency as compared to other forms of strut-based and skeletal-based lattice structures. This study presents experimental and computational evidence of the robustness and suitability of sheet-based IWP structures for different engineering applications, where strong and lightweight materials with exceptional energy absorption capabilities are required.