Lidinoid

Triply periodic minimal surface
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 a Schwarz H surface.[2] It belongs to space group 230(Ia3d).

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

( 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 {\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". Archived from the original on 2012-12-20. Retrieved 2012-09-15.

External images

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