Simoes-Batista Surface (genus 7)
Simoes-Batista Surface (genus 7) 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
Genus-7 triply periodic 1-parameter family with rectangular period lattice, obtained by adding a handle to Batista's triply periodic Costa surface; limits are the singly periodic CHM(1,3) surface and the doubly periodic Scherk surface.
Sources
Derived from the Math Art generator registries and cross-referenced to the literature; not transcribed from any gallery's compilation.
- 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**)]
- 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]
- 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]
- J. W. Fisher, S. W. Miller, J. Bartolai, T. W. Simpson, M. A. Yukish, "Catalog of triply periodic minimal surfaces, equation-based lattice structures, and their homogenized property data", Data in Brief 49 (2023) 109311. doi:10.1016/j.dib.2023.109311 [equation compilation; K, Q*, Triplane/F recommendations]
- M. Weber, 'The Simoes-Batista Surface', minimalsurfaces.blog (local mirror: minsurf/book/.../ch408_the_simoes_batista_surface.md).
- P. Simoes and V. Ramos Batista, arXiv:0806.3088 (2008), the paper the mirrored page links.