Schoen-Karcher T-Wp (hexagonal wrapped package)
Schoen-Karcher T-Wp (hexagonal wrapped package) 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
A hexagonal triply periodic minimal surface family that 3DXM exhibits as 'A Schoen TW Family': Karcher's T-Wp ('wrapped package') surface, made in Schoen's spirit but not in the NASA report; the alpha = beta = 60-degree member of the conjugate-contour family whose 45-degree member is I-WP.
Sources
Derived from the Math Art generator registries and cross-referenced to the literature; not transcribed from any gallery's compilation.
- A. H. Schoen, "Infinite periodic minimal surfaces without self-intersections", NASA TN D-5541 (1970). [O,C-TO]
- H. Karcher, "The triply periodic minimal surfaces of Alan Schoen and their constant mean curvature companions", Manuscripta Math. 64 (1989) 291-357. doi:10.1007/BF01165824 [K surface]
- 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]
- The 3DXM Consortium, 'A Schoen TW Family', Virtual Math Museum, virtualmathmuseum.org (local mirror: vmm/book/surface/ch037_schoen_tw.md).
- A. H. Schoen, 'Infinite periodic minimal surfaces without self-intersections', NASA Technical Note TN D-5541 (1970).
- H. Karcher, 'The triply periodic minimal surfaces of Alan Schoen and their constant mean curvature companions', Manuscripta Math. 64 (1989) 291-357, sections 5.3.3/5.4.4 (T-Wp) and 6.2 (the two-angle family joining it to I-WP).