Coxeter Groups in Colored Tilings and Patterns

Aus de_evolutionary_art_org
Wechseln zu: Navigation, Suche


Reference

Glenn R. Laigo, Ia Kristine D. Puzon and and Ma. Louise Antonette N. De Las Peñas: Coxeter Groups in Colored Tilings and Patterns. In: Bridges 2008. Pages 311–318

DOI

Abstract

This paper illustrates a number of ways that color symmetry theory can be used as a tool to study abstract groups such as Coxeter groups.

Extended Abstract

Bibtex

Used References

[1] Coxeter, H.S.M. Coloured Symmetry, in M.C. Escher Art and Science, The Netherlands, H.S.M. Coxeter, et al., Eds, 15 – 33 (Elsevier Science Publishers B.V., The Netherlands, 1985).

[2] Coxeter, H.S.M. Discrete Groups Generated by Reflections, in The Annals of Mathematics, 2nd Ser. Vol. 35, No. 3, 588 – 621 (1934).

[3] Coxeter, H.S.M. Twisted Honeycombs, Regional Conference Series in Mathematics No. 4. USA: American Mathematical Society (1970).

[4] Coxeter, H.S.M. and W.O. Moser. Generators and Relations for Discrete Groups, 2nd ed. USA: Springer-Verlag (1965).

[5] Cubic Honeycomb. http://en.wikipedia.org/wiki/Image:Cubic_honeycomb.png.

[6] Decena, M.C.B. On The Index 3 and 4 Subgroups of Triangle Groups, a PhD Dissertation, Ateneo de Manila University (2007).

[7] De Las Peñas, M.L.A.N., R. Felix and G. Laigo, Colorings of Hyperbolic Plane Crystallographic Patterns, in Z. Kristallogr 221, 665 – 672 (2006).

[8] De Las Peñas, M.L.A.N., G. Laigo and E. Provido, Studying Non-Euclidean Tilings and their Groups with the Aid of Technology, in Proceedings of the Eleventh Asian Technology Conference in Mathematics ATCM 2006, Hong Kong, W.C. Yang, et al., Eds, 317 – 326 (ATCM, Inc., USA, 2006)

[9] De Las Peñas, M.L.A.N., G. Laigo and E. Provido, Hyperbolic Semi-Regular Tilings and their Symmetry Properties, in Bridges Donostia: Mathematical Connections in Art, Music and Science Proceedings 2007, R. Sarhangi and J. Barallo, eds. UK: Tarquin Publications (2007).

[10] De Las Peñas, M.L.A.N., R. Felix and E. Provido, On Index 2 Subgroups of Hyperbolic Symmetry Groups, in Z. Kristallogr 222, 443 – 448 (2007).

[11] Dunham, D, H.S.M. Coxeter and Tony Bomford’s Colored Hyperbolic Rugs, in Renaissance Banff, Bridges: Mathematical Connections in Art, Music, and Science Proceedings 2005, R. Sarhangi, ed. USA: Central Plain Book Manufacturing (2005).

[12] _____, Transformation of Hyperbolic Escher Patterns, in Visual Mathematics, Volume 1, No 1, (1999). http://www.d.umn.edu/~ddunham/isis4/index.html.

[13] Magnus, W. Non-Euclidean Tesselations and their Groups. USA: Academic Press Inc (1974).

[14] Grove, L.C. and C.T. Benson. Finite Reflection Groups, 2nd ed, Graduate Texts in Mathematics 99, USA: Springer-Verlag (1985).

[15] Hernandez, N.H.S. On Colorings Induced by Low Index Subgroups of Some Hyperbolic Triangle Groups, a Masters Thesis, University of the Philippines – Diliman (2003).

[16] Humphreys, J.E. Reflection Groups and Coxeter Groups, Cambridge Studies in Advanced Mathematics 29. UK: Cambridge University Press (1990).

[17] Leys, J. The Creatures. (2006). http://www.josleys.com/show_image.php?image=Escher/escher031.jpg&name=Creatures2.

[18] Mackenzie, D. A Hyperbolic Plane Coloring and the Simple Group of Order 168, in The American Mathematical Monthly, Vol 102, No 8 706 – 715 (1995).

[19] Pickett, B.S. Monreale, http://art-uo.uoregon.edu/faculty/gallery/show.cfm?image=29.

[20] Schwarzenberger, R.L.E. Colour Symmetry, in Bulletin of the London Mathematical Society, 16, 209 – 240 (1984).

[21] Senechal, M. Color Symmetry, in Computers & Mathematics with Applications, 16, 5 – 8, 545 – 553 (1988).

[22] Van Der Waerden, B.L. and J.J. Burckhardt, Farbgruppen, in Z. Kristallogr 115, 231 – 234 (1961).


Links

Full Text

http://archive.bridgesmathart.org/2008/bridges2008-311.pdf

intern file

Sonstige Links

http://archive.bridgesmathart.org/2008/bridges2008-311.html