Saddle Polyhedron
Saddle Polyhedron is a discrete surface, given by a parametrisation, immersed.
Open Saddle Polyhedron in the interactive viewer →
aperiodic def-parametric discrete immersed implemented
Properties
- Family
- discrete
- Given by
- a parametrisation
- Curvature
- no condition imposed
- Periodicity
- not periodic
- Ends
- 0
- Embedding
- immersed
- Fidelity
- exact
Definition
No chart is stored: bounded by numerically relaxed saddle-polygon patches (see pearce-saddle-surface); also piecewise, one patch per face. The shipped implementation 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.
- Peter Pearce, "Structure in Nature is a Strategy for Design", The MIT Press, 1978 (paperback 1990), ch. 8 -- the Universal Node system, saddle polygons spanned by minimal surfaces, and Table 8.1's inventory of 53 saddle polyhedra.
- Walt van Ballegooijen, Paul Gailiunas & Daniel Erdely, "Spidronised Space-fillers", Bridges 2009 Conference Proceedings, pp. 271-278 -- spidron nests on saddle-polyhedron faces and the rule that clockwise must meet counter-clockwise across a shared face.
- Daniel Erdely, "Some Surprising New Properties of the Spidrons", Bridges 2005 Conference Proceedings, pp. 179-186 -- the spidron nest the face decoration generalises.
- Ulrich Pinkall & Konrad Polthier, "Computing Discrete Minimal Surfaces and Their Conjugates", Experimental Mathematics 2(1), 1993, pp. 15-36 -- the cotangent-Laplacian area minimisation used for the saddle faces.