Schoen I-WP

Schoen I-WP is a triply periodic minimal surface, defined as a nodal algebraic surface, genus 4 per unit cell, immersed, with Im-3m symmetry (a crystallographic space group).

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def-nodal has-approximation immersed implemented minimal minimal-periodic tradition-crystallographic triply-periodic

Formula

2 \left(\cos\left(x\right) \cos\left(y\right) + \cos\left(y\right) \cos\left(z\right) + \cos\left(z\right) \cos\left(x\right)\right) - \left(\cos\left(2 x\right) + \cos\left(2 y\right) + \cos\left(2 z\right)\right) = 0

Properties

Family: minimal-periodic
Given by: a nodal algebraic surface
Curvature: zero mean curvature
Periodicity: triply periodic
Genus per cell: 4
Ends: 0
Embedding: immersed
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.

A. H. Schoen, "Infinite periodic minimal surfaces without self-intersections", NASA TN D-5541 (1970) -- gyroid, I-WP, F-RD.
H. A. Schwarz (P, D; Gesammelte Mathematische Abhandlungen, 1890).
E. R. Neovius (1883). Inventory and nodal equations after Ken Brakke's periodic-surface pages (kenbrakke.com/evolver); the tier-2 sources are documented at the expansion block below.