Lidinoid

Lidinoid in a unit cell.

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 the Schwarz H surface.^[2] It belongs to space group 230(Ia3d).

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

${\displaystyle {\begin{aligned}(1/2)[&\sin(2x)\cos(y)\sin(z)\\+&\sin(2y)\cos(z)\sin(x)\\+&\sin(2z)\cos(x)\sin(y)]\\-&(1/2)[\cos(2x)\cos(2y)\\+&\cos(2y)\cos(2z)\\+&\cos(2z)\cos(2x)]+0.15=0\end{aligned}}}$

References

1. Lidin, Sven; Larsson, Stefan (1990). "Bonnet Transformation of Infinite Periodic Minimal Surfaces with Hexagonal Symmetry". J. Chem Soc. Faraday Trans. 86 (5): 769–775. doi:10.1039/FT9908600769.
2. Adam G. Weyhaupt (2008). "Deformations of the gyroid and lidinoid minimal surfaces". Pacific Journal of Mathematics. 235 (1): 137–171. doi:10.2140/pjm.2008.235.137.
3. The lidionoid in the Scientific Graphic Project

External images

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