Schwarz's minimal surface is a periodic minimal surface
constructed using the following two principles:
1. If part of the boundary of a minimal surface is a straight line, then the reflection across the line, when added to the original
surface, makes another minimal surface .
2. If a minimal surface meets a plane at right angles , then the mirror image of the plane ,
when added to the original surface, also makes a minimal
surface .
Surfaces similar to Schwarz's minimal surface have been cited among architectural applications of minimal surfaces (Bock Hyeng et
al. 2025).
See also Minimal Surface ,
Neovius
Minimal Surface
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References Bock Hyeng, C. A.; Krivoshapko, S. N.; Kouamou Nguessi, A.; Yamb Bell, E.; and Bahel, B. "Application of Curvilinear Analytical
Surfaces in Forms of Architectural Objects and Machine Building Products." Int.
J. Archit. Arts Appl. 11 , 19-35, 2025. https://doi.org/10.11648/j.ijaaa.20251101.13 . GRAPE.
"Schwarz's P-Surface and Deformation (Hermann Amandus Schwarz)." https://archive.ins.uni-bonn.de/numod.ins.uni-bonn.de/grape/EXAMPLES/AMANDUS/schwarz.html . Wells,
D. The
Penguin Dictionary of Curious and Interesting Geometry. Referenced on Wolfram|Alpha Schwarz's Minimal Surface
Cite this as:
Weisstein, Eric W. "Schwarz's Minimal Surface."
From MathWorld https://mathworld.wolfram.com/SchwarzsMinimalSurface.html
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