Triply Periodic Costa (Batista, exact fundamental piece, genus 5)
Triply Periodic Costa (Batista, exact fundamental piece, genus 5) is a triply periodic minimal surface, given by a Weierstrass representation, genus 4 per unit cell, embedded, with a crystallographic space group.
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def-weierstrass embedded 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
- 4
- Ends
- 0
- Embedding
- embedded
- Symmetry kind
- crystallographic space group
- Fidelity
- exact
- Exactness
- numerical-integral
Definition
No closed form is stored for this surface. It is defined by its shipped implementation in math_art.minsurf.tpms, which 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.
- 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, https://minimalsurfaces.blog/ and the archive formerly at indiana.edu/~minimal/archive/ (the site is dead; 280 surface folders were recovered from the Wayback CDX index).