RESUMO
Schwarzites are porous (spongy-like) carbon allotropes with negative Gaussian curvatures. They are proposed by Mackay and Terrones inspired by the works of the German mathematician Hermann Schwarz on Triply-Periodic Minimal Surfaces (TPMS). This review presents and discusses the history of schwarzites and their place among curved carbon nanomaterials. The main works on schwarzites are summarized and are available in the literature. Their unique structural, electronic, thermal, and mechanical properties are discussed. Although the synthesis of carbon-based schwarzites remains elusive, recent advances in the synthesis of zeolite-templates nanomaterials have brought them closer to reality. Atomic-based models of schwarzites are translated into macroscale ones that are 3D-printed. These 3D-printed models are exploited in many real-world applications, including water remediation and biomedical ones.