Eight-Ended Scherk Tower (genus 2)
Eight-Ended Scherk Tower (genus 2) is a singly periodic minimal surface, given by a Weierstrass representation, genus 2, 8 ends, immersed, with a rod group.
Open Eight-Ended Scherk Tower (genus 2) in the interactive viewer →
def-weierstrass immersed implemented minimal minimal-periodic singly-periodic tradition-classical
Properties
- Family
- minimal-periodic
- Given by
- a Weierstrass representation
- Curvature
- zero mean curvature
- Periodicity
- singly periodic
- Genus
- 2
- Ends
- 8
- Embedding
- immersed
- Symmetry kind
- rod group
- Fidelity
- exact
- Exactness
- numerical-integral
Definition
No (g, dh) pair is stored: the shipped row is built by the dedicated mesher we.sscherk_eight_mesh (a torus/branched-cover or multi-patch assembly); no elementary (g, dh) pair on a plane domain is stored in the code. The shipped implementation is authoritative; an unverified transcription would silently define a different surface.
Sources
Derived from the Math Art generator registries and cross-referenced to the literature; not transcribed from any gallery's compilation.
- H. Karcher, Manuscripta Math. 62 (1988); H. F. Scherk (1835);
- K. Li thesis lineage (6/8-ended towers); L. daSilva, V. Ramos Batista (2009); M. Weber, https://minimalsurfaces.blog/ notebooks Singly_6ended_Scherk_g1.nb, Singly_CostaScherk_g1.nb, Singly_8ended_Scherk_g2.nb, Singly_daSilvaBatista_g2.nb (research/msblog_harvest/singly_periodic.json). Full scholarly details in the weierstrass sscherk block header.