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Artifacts for Stamping Symmetric Designs.

Montesinos Amilibia, José María and Hilden, Hugh Michael and Tejada Jiménez, Débora María and Toro Villegas, Margarita María (2011) Artifacts for Stamping Symmetric Designs. American Mathematical Monthly, 118 (4). pp. 327-343. ISSN 0002-9890

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Official URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.118.04.327

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Abstract

It is well known that there are 17 crystallographic groups that determine the possible tessellations of the Euclidean plane. We approach them from an unusual point of view. Corresponding to each crystallographic group there is an orbifold. We show how to think of the orbifolds as artifacts that serve to create tessellations.


Item Type:Article
Uncontrolled Keywords:crystallographic groups; fundamental domains; Moebius strip; orbifolds; symmetry group; tesselations
Subjects:Sciences > Chemistry > Crystallography
Sciences > Mathematics > Geometry
ID Code:16947
References:

F. Bonahon and L. Siebenmann, The classification of Seifert fibred 3-orbifolds, in Low Dimensional Topology–Chelwood Gate 1982, London Math. Soc. Lecture Note Ser., vol. 95, Cambridge University Press, Cambridge, 1985, 19–85.

M. V. Gutiérrez-Santos, Notas de Geometría, Universidad Nacional de Colombia, Bogotá, 1992.

H. M. Hilden, J. M. Montesinos, D. M. Tejada, and M. M. Toro, Dise~nos geométricos en la obra de Escher, 2009 (preprint).

C. Klein and C. S. Hurlbut, Jr., Manual of Mineralogy (after J. D. Dana), 21st rev. ed., John Wiley, New York, 1999.

J. M. Montesinos, Classical Tessellations and Three-Manifolds, Springer-Verlag, Berlin, 1987.

J. M. Montesinos, Calidoscopios y 3-Variedades, Universidad Nacional de Colombia, Bogotá, 2003.

J. M. Montesinos, Geometría en los Mosaicos del Palacio de la Alhambra de Granada, Conferencia, Cátedra Pedro Nel Gómez, Centro Audiovisual de la Universidad Nacional de Colombia Sede Medellín, Colombia, 2005.

J. M. Montesinos, La cristalografía geométrica, in Horizontes Culturales. Las Fronteras de la Ciencia, Real Academia de las Ciencias Exactas, Físicas y Naturales de Espa~na, eds., Editorial Espasa, Madrid, 1999, 97–112.

A. I. Ramírez-Galarza and J. Seade, Introduction to Classical Geometries, Birkhäuser, Berlin, 2002.

D. Seymour and J. Britton, Introduction to Tessellations, Dale Seymour, Palo Alto, CA, 1989.

W. Thurston, Three-Dimensional Geometry and Topology, vol. 1, S. Levy, ed., Princeton University Press, Princeton, NJ, 1997

Deposited On:31 Oct 2012 09:11
Last Modified:31 Oct 2012 09:11

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