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== Reference ==
Domingo Gámez, Miguel Pasadas, Rafael Pérez and Ceferino Ruiz: [[NEC Polygonal Groups and Tessellations]]. In: [[Bridges 2003]]. Pages 299–306

== DOI ==

== Abstract ==
A kaleidoscope is obtained as the quotient of a space by the discontinuous action of a discrete group
of transformations; this can also be obtained from a fundamental domain which characterizes it. In
the present study, the specific case of the Hyperbolic Plane is analyzed with respect to the I).ction of
a hyperbolic polygonal group, which is a particular case of an NEC group. Under the action of these
groups, the hyperbolic plane is tessellated using tiles with a polygonal shape. The generators of the
group are reflections in the sides of the polygon. Clear examples of quadrilateral tessellations of the
hyperbolic plane with Saccheri and Lambert quadrilaterals -designed using the Hyperbol package created
for Mathematica software- and are found in the basic structure of some of the mosaics of M.C. Escher.

== Extended Abstract ==

== Bibtex ==

== Used References ==
A.F. Beardon, Hyperbolic polygons and Fuchsian groups, J. London Math. Soc., Vol. 20, pp.
247-255. 1979.

[2] M. C. Escher, Regelmatige vlakverdeling, Stichting 'De Roos', Utrech, 1958.

[3] D. Gamez, Gonstrucciones en Geomema Hiperb61ica y Teselaciones mediante Grupos NEG
Poligonales. Algoritmos de Automatizacion, PhD Thesis, Granada, 2001.

[4] D. Gamez, M. Pasadas, R. Perez, C. Ruiz, Hyperbolic Plane Tesselations. Proceedings of the VI
Journees Zaragoza-Pau de Mathematiques Appliquees et Statistique, pp. 257-264, Jaca, Spain,
1999.

[5] D. Gamez, M.Pasadas, R. Perez, C. Ruiz, Regla y compas hiperb6licos electronicos para teselar.
Proceedings of the I Encuentro de Matematicos Andaluces, Vol. 2, pp.:467-474, Sevilla, 2000.

[6] D. Gamez, M. Pasadas, R. Perez, C. Ruiz, The Lambert quadrilateral and tesselations in the
hyperbolic plane. Int. Math. J., Vol. 2, pp. 777-795, 2002.

[7] D. Gamez, M. Pasadas, R. Perez, C. Ruiz, The Saccheri Quadrilateral, Translations and Tes-
selations in the Hyperbolic Plane (Submitted).

[8] M. J. Greenberg, Euclidean and non-Euclidean geometries: development and history, 3rd Edi-
tion, W. H. Freeman & Co., New York, 1993.

[9] A. M. Macbeath, The classification of non-Euclidean plane crystallographic groups, Canadian
J. Math., Vol. 19, pp. 1192-1205, 1967.

[10] E. Martinez, Convex Fundamental Regions for NEG Groups, Arch. Math., Vol. 47, pp. 457-464,
1986.

[11] R.perez Gomez, Espacios Gromaticos. PhD Thesis, Granada, 1992.

[12] H. C. Wilkie, On Non-Euclidean Crystallographic Groups, Math. Z., Vol. 91, pp.87-102, 1966.

[13] Haags Gemeentemuseum, M. G. Escher (1898-1972). Regelmatige Vlakverdelingen in het Haags
Gemmentemuseum (Regular divisions of the plane at the Haags Gemeentemuseum), Snoeck-
Ducaju & Zoon, Gent, 1986.

[14] Koninklijke Erven J.J. Tijl N.V., M. G. Escher "Grafiek en Tekeningen", Zwolle, 1959.

== Links ==
=== Full Text ===
http://archive.bridgesmathart.org/2003/bridges2003-299.pdf

[[intern file]]

=== Sonstige Links ===
http://archive.bridgesmathart.org/2003/bridges2003-299.html

NEC Polygonal Groups and Tessellations - Versionsgeschichte

Gbachelier: Die Seite wurde neu angelegt: „ == Reference == Domingo Gámez, Miguel Pasadas, Rafael Pérez and Ceferino Ruiz: NEC Polygonal Groups and Tessellations. In: Bridges 2003. Pages 299…“