Wei Triply Periodic Surface (genus 4, a=0.1 b=0.3 member)
Wei Triply Periodic Surface (genus 4, a=0.1 b=0.3 member) is a triply periodic minimal surface, given by a Weierstrass representation, immersed, with 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
- Ends
- 0
- Embedding
- immersed
- Symmetry kind
- crystallographic space group
- Fidelity
- exact
- Exactness
- numerical-integral
Definition
Wei's 2-parameter family of genus-4 triply periodic minimal surfaces from his 1992 doubly periodic paper; his doubly periodic genus-2 surfaces (which have their own record) arise as limits, as do vertical planes over a rhombic tiling desingularized by singly periodic Scherk surfaces. THE SHIPPED ROW IS THE (a, b) = (0.1, 0.3) MEMBER -- the one the notebook renders -- with the modulus re-derived from its period integral (tau = 0.849141499409681i); the notebook pins no canonical member of the family, and the built cell measures 0.771 : 0.815 : 1, so it is NOT the square-based special member the page pictures suggest.
Sources
Derived from the Math Art generator registries and cross-referenced to the literature; not transcribed from any gallery's compilation.
- M. Wohlgemuth, N. Yufa, J. Hoffman, E. L. Thomas, "Triply periodic bicontinuous cubic microdomain morphologies by symmetries", Macromolecules 34 (2001) 6083-6089. doi:10.1021/ma0019499 [O,C-TO (OCTO), G', F-RD variant]
- E. Koch and W. Fischer, "Triply periodic minimal balance surfaces: a correction", Acta Crystallogr. A 49 (1993) 209-210. doi:10.1107/S0108767392007591 [C(S) = P and Y = D as minimal surfaces; the nodal geometries remain distinct]
- H. G. von Schnering and R. Nesper, "Nodal surfaces of Fourier series: fundamental invariants of structured matter",
- Z. Phys. B Condensed Matter 83 (1991) 407-412. doi:10.1007/BF01313411 [C(D), C(Y), +-Y, C(+-Y), S nodal forms]
- H. G. von Schnering, M. Oehme, G. Rudolf, "Three-dimensional periodic nodal surfaces which envelope the threefold and fourfold cubic rod packings", Acta Chem. Scand. 45 (1991) 873-876. doi:10.3891/acta.chem.scand.45-0873 [C(I2-Y**)]
- D. A. Hoffman, J. T. Hoffman, M. Weber, et al., "Table of Surfaces", The Scientific Graphics Project, MSRI (2003). [D' and further G'/OCTO forms]
- M. Weber, 'Wei's Triply Periodic Surface of Genus 4', minimalsurfaces.blog (local mirror: minsurf/book/.../ch335_weis_triply_periodic_surface_of_genus_4.md).
- F. Wei, 'Some existence and uniqueness theorems for doubly periodic minimal surfaces', Invent. Math. 109 (1992) 113-136.