Department of Physics, Quaid-e-Azam University
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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}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/38cfb4463becbc12585998256442df47a46b08f2)
References
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External images
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- ↑ Sven Lidin and Stefan Larsson, Bonnet Transformation of Infinite Periodic Minimal Surfaces with Hexagonal Symmetry, J. Chem Soc. Faraday Trans, 1990, 86(5), 769–775
- ↑ Adam G. Weyhaupt, Deformations of the gyroid and lidinoid minimal surfaces. Pacific Journal of Mathematics. Vol. 235 (2008), No. 1, 137–171
- ↑ The lidionoid in the Scientific Graphic Project