Crooked Houses: Visualizing the Polychora with Hyperbolic Patchwork
Inhaltsverzeichnis
Referenz
Taneli Luotoniemi: Crooked Houses: Visualizing the Polychora with Hyperbolic Patchwork. In: Bridges 2017, Pages 17–24.
DOI
Abstract
This paper presents kinetic models based on the 4-dimensional regular polytopes. The sequential ‘flattening’ is realized through the use of hyperbolic patchwork surfaces, which portray the bitruncated versions of the polychora. As pedagogical tools, these models offer a hands-on experience of 4D geometry.
Extended Abstract
Bibtex
@inproceedings{bridges2017:17,
author = {Taneli Luotoniemi},
title = {Crooked Houses: Visualizing the Polychora with Hyperbolic Patchwork},
pages = {17--24},
booktitle = {Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture},
year = {2017},
editor = {David Swart, Carlo H. S\'equin, and Krist\'of Fenyvesi},
isbn = {978-1-938664-22-9},
issn = {1099-6702},
publisher = {Tessellations Publishing},
address = {Phoenix, Arizona},
note = {Available online at \url{http://archive.bridgesmathart.org/2017/bridges2017-17.pdf}}
}
Used References
[1] H. S. M. Coxeter. Regular Polytopes. Dover Publications. 1973.
[2] Robert A. Heinlein, “…And He Built a Crooked House”, In Astounding Science Fiction, February 1941.
[3] Saul Scleimer and Henry Segerman. Sculptures in S³. In Robert Bosch, Douglas McKenna, and Reza Sarhangi, editors, Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture, pages 103–110, Phoenix, Arizona, 2012, Tessellations Publishing. Available online at http://archive.bridgesmathart.org/2012/bridges2012-103.html
[4] Carlo H. Séquin. 3D Visualization Model of the Regular Polytopes in Four and Higher Dimensions. In Reza Sarhangi, editors, Bridges: Mathematical Connections in Art, Music, and Science, pages 37–48, Southwestern College, Winfield, Kansas, 2002, Bridges Conference. Available online at http://archive.bridgesmathart.org/2002/bridges2002-37.html
[5] Jeffrey R. Weeks. How To Sew a Hyperbolic Blanket. http://www.geometrygames.org/HyperbolicBlanket/index.html (as of April 21, 2017)
[6] Jeffrey R. Weeks. The Shape of Space. CRC Press. 2001.
[7] Wikipedia Contributors. Uniform 4-polytope. https://en.wikipedia.org/wiki/Uniform_4-polytope (as of April 21, 2017)
Links
Full Text
http://archive.bridgesmathart.org/2017/bridges2017-17.pdf
