Order 3 Neovius Surface
Order 3 Neovius Surface is a triply periodic minimal surface, given by a Weierstrass representation, genus 13 per unit cell, immersed, with a crystallographic space group.
Open Order 3 Neovius Surface in the interactive viewer →
def-weierstrass immersed minimal minimal-periodic not-implemented tradition-crystallographic triply-periodic
Properties
- Family
- minimal-periodic
- Given by
- a Weierstrass representation
- Curvature
- zero mean curvature
- Periodicity
- triply periodic
- Genus per cell
- 13
- Ends
- 0
- Embedding
- immersed
- Symmetry kind
- crystallographic space group
- Fidelity
- exact
Definition
No closed form is stored: the surface is not implemented in math_art, so there is no shipped code to verify a transcription against, and an unverified formula from the literature would be worse than a null. See construction.blocked_by.
Not yet built
This surface is catalogued but not yet built by the extension, so it has no mesh or thumbnail here.
Sources
Not transcribed. The record exists to state that the surface is absent and why; a fabricated equation would be worse than a null.
- M. Weber, https://minimalsurfaces.blog/ and the archive formerly at indiana.edu/~minimal/archive/ (the site is dead; 280 surface folders were recovered from the Wayback CDX index).
- M. Weber, 'Order 3 Neovius Surface', formerly at indiana.edu/~minimal/archive/Triply/genus13/Neoviussym3/ (Wayback capture 2010-07-27; page and renders preserved in the local mirror).
- H. Karcher, 'The triply periodic minimal surfaces of Alan Schoen and their constant mean curvature companions', Manuscripta Math. 64 (1989) 291-357, section 6.1.3 -- the Neovius analogs with handles to the horizontal edges of the three orthogonal prisms.