Lidinoid (exact)
Lidinoid (exact) is a triply periodic minimal surface, given by a Weierstrass representation, genus 3 per unit cell, immersed, with Ia-3d symmetry (a crystallographic space group).
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def-weierstrass immersed implemented minimal minimal-periodic tradition-crystallographic triply-periodic
Properties
- Family
- minimal-periodic
- Given by
- a Weierstrass representation
- Curvature
- zero mean curvature
- Periodicity
- triply periodic
- Genus per cell
- 3
- Ends
- 0
- Embedding
- immersed
- Symmetry
- Ia-3d
- Symmetry kind
- crystallographic space group
- Fidelity
- exact
- Exactness
- numerical-integral
Definition
No (g, dh) pair is stored: the Gauss map is a product of powers of Jacobi theta functions on the hexagonal/square torus, continued along an unwrapped branch (math_art/minsurf/hexagonal.py); theta functions are outside the exact expression language. 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. 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.