Lidinoid

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Short description: 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⁡(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

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". https://secure.msri.org/about/sgp/jim/papers/morphbysymmetry/lidinoid/index.html. 

External images