The gyroid is the unique non-trivial embedded member of the associate family of the Schwarz P and D surfaces with angle of association approximately 38.01°. The gyroid is similar to the Lidinoid. The gyroid was discovered in 1970 by NASA scientist Alan Schoen. He calculated the angle of association and gave a convincing demonstration pictures of intricate plastic models, but did not provide a proof of embeddedness. Schoen noted that the gyroid contains neither straight lines nor planar symmetries. Karcher[3] gave a different, more contemporary treatment of the surface in 1989 using conjugate surface construction. In 1996 Große-Brauckmann and Wohlgemuth[4] proved that it is embedded, and in 1997 Große-Brauckmann provided CMC variants of the gyroid and made further numerical investigations about the volume fractions of the minimal and CMC gyroids.

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