  Schwarzites are porous (spongy-like) carbon allotropes with negative Gaussian
curvatures. They were 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. We summarized the main works on
schwarzites available in the literature. We discuss their unique structural,
electronic, thermal, and mechanical properties. Although the synthesis of
carbon-based schwarzites remains elusive, the recent advances in the synthesis
of zeolite-templates nanomaterials bring them closer to reality. Atomic-based
models of schwarzites have been translated into macroscale ones that have been
3D printed. These 3D printed models have been exploited in many real-world
applications, including water remediation and biomedical ones.
