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Metallic-glass-matrix composites demonstrating unusual combination of high strength, high toughness, and excellent processability are utilized to fabricate cellular structures of egg-box topology. Under compressive loading, the egg-box panels are capable of undergoing extensive plastic collapse at very high plateau stresses enabling absorption of large amounts of mechanical energy. In terms of specific mechanical energy absorbed, the present panels far outperform panels of similar topology made of aluminum or fiber-reinforced polymer composites, and even surpass steel structures of highly buckling-resistant topologies, thus emerging among the highest performance structures of any kind.