Neovius

Neovius is a triply periodic minimal surface, defined as a nodal algebraic surface, genus 9 per unit cell, embedded, with Im-3m symmetry (a crystallographic space group).

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def-nodal embedded has-approximation implemented minimal minimal-periodic tradition-classical tradition-crystallographic triply-periodic

Formula

3 \left(\cos\left(x\right) + \cos\left(y\right) + \cos\left(z\right)\right) + 4 \cos\left(x\right) \cos\left(y\right) \cos\left(z\right) = 0

Properties

Family: minimal-periodic
Given by: a nodal algebraic surface
Curvature: zero mean curvature
Periodicity: triply periodic
Genus per cell: 9
Ends: 0
Embedding: embedded
Orientable: yes
Symmetry: Im-3m
Symmetry kind: crystallographic space group
Fidelity: approximation

Definition

Standard nodal approximation as shipped in math_art/minsurf/tpms.py. No exact definition is stored for this surface, so this approximation is all the record has; `approximates` is null rather than pointing at itself.

Sources

Derived from the Math Art generator registries and cross-referenced to the literature; not transcribed from any gallery's compilation.

E. R. Neovius, 'Bestimmung zweier speciellen periodischen Minimalflachen', Helsingfors (1883).
M. Weber, minimalsurfaces.blog, 'Neovius Surface' (mirror: minsurf ch275): the X-pieces 'extend to the edges of a cube, making it a genus 9 surface' -- independent genus-per-cell oracle.