Lidinoid Explained

In differential geometry, the lidinoid is a triply periodic minimal surface. The name comes from its Swedish discoverer Sven Lidin (who called it the HG surface).^[1]

It has many similarities to the gyroid, and just as the gyroid is the unique embedded member of the associate family of the Schwarz P surface the lidinoid is the unique embedded member of the associate family of a Schwarz H surface.^[2] It belongs to space group 230(Ia3d).

The Lidinoid can be approximated as a level set:^[3]

\begin{align} ( 1 / 2 )[&\sin( 2 x) \cos(y)\sin(z)\\ + &\sin( 2 y)\cos(z) \sin(x)\\ + &\sin( 2 z)\cos(x) \sin(y)]\ - & ( 1 / 2 )[\cos( 2 x)\cos( 2 y)\\ + &\cos( 2 y)\cos( 2 z)\\ + &\cos( 2 z)\cos( 2 x)] + 0 . 15 = 0 \end{align}

External images

• The lidinoid at the minimal surface archive
• The lidinoid in the Scientific Graphic Project

Notes and References

1. Sven . Lidin . Stefan . Larsson . Bonnet Transformation of Infinite Periodic Minimal Surfaces with Hexagonal Symmetry . J. Chem. Soc. Faraday Trans. . 1990 . 86 . 5 . 769–775 . 10.1039/FT9908600769.
2. Adam G. Weyhaupt . Deformations of the gyroid and lidinoid minimal surfaces . Pacific Journal of Mathematics . 235 . 2008 . 1 . 137–171 . 10.2140/pjm.2008.235.137. free .
3. Web site: The lidionoid in the Scientific Graphic Project . 2012-09-15 . https://archive.today/20121220224223/https://secure.msri.org/about/sgp/jim/papers/morphbysymmetry/lidinoid/index.html . 2012-12-20 . dead .