Scherk Tower (singly periodic)

Scherk Tower (singly periodic) is a triply periodic minimal surface, defined as a nodal algebraic surface, immersed, with P42/mcm symmetry (a crystallographic space group).

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

Formula

\sin\left(z\right) - \sinh\left(x\right) \sinh\left(y\right) = 0

Properties

Family: minimal-periodic
Given by: a nodal algebraic surface
Curvature: zero mean curvature
Periodicity: triply periodic
Ends: 0
Embedding: immersed
Orientable: yes
Symmetry: P42/mcm
Symmetry kind: crystallographic space group
Fidelity: exact
Exactness: elementary

Definition

Standard nodal approximation as shipped in math_art/minsurf/tpms.py.

Sources

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

H. A. Schwarz (P, D; Gesammelte Mathematische Abhandlungen, 1890).
A. H. Schoen, "Infinite periodic minimal surfaces without self-intersections", NASA TN D-5541 (1970) -- gyroid, I-WP, F-RD.
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.