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Inhaltsverzeichnis
Reference
Saul Schleimer and Henry Segerman: Sculptures in S3. In: Bridges 2012. Pages 103–110
DOI
Abstract
We construct a number of sculptures, each based on a geometric design native to the three-dimensional sphere. Using stereographic projection we transfer the design from the three-sphere to ordinary Euclidean space. All of the sculptures are then fabricated by the 3D printing service Shapeways.
Extended Abstract
Bibtex
Used References
[1] Alan F. Beardon, The geometry of discrete groups, Graduate Texts in Mathematics, vol. 91, Springer- Verlag, New York, 1983.
[2] John H. Conway and Derek A. Smith, On quaternions and octonions: their geometry, arithmetic, and symmetry, A K Peters Ltd., Natick, MA, 2003.
[3] H. S. M. Coxeter, Regular polytopes, third ed., Dover Publications Inc., New York, 1973.
[4] Manfredo Perdigão do Carmo, Riemannian geometry, Mathematics: Theory & Applications, Birkhäuser Boston Inc., Boston, MA, 1992, Translated from the second Portuguese edition by Francis Flaherty.
[5] George W. Hart, 4d polytope projection models by 3d printing, to appear in Hyperspace.
[6] H. Blaine Lawson, Complete minimal surfaces in S3 , Annals of Mathematics 92 (1970), no. 3, 335–374.
[7] D. Lerner and D. Asimov, The Sudanese Möbius band (video), In SIGGRAPH Video Review, 1984.
[8] Fritz H. Obermeyer, Jenn3d, a computer program for visualizing Coxeter polytopes, available from http://www.math.cmu.edu/~fho/jenn/
[9] Adrian Ocneanu, Octacube, http://science.psu.edu/news-and-events/2005-news/math10-2005.htm.
[10] Charles Perry, Zero, http://www.charlesperry.com/sculpture/zero.
[11] Günter M. Ziegler, Lectures on polytopes, Graduate Texts in Mathematics, vol. 152, Springer-Verlag, New York, 1995.
Links
Full Text
http://archive.bridgesmathart.org/2012/bridges2012-103.pdf
