http://de.evo-art.org/index.php?action=history&feed=atom&title=Counterchange_Patterns_and_Polyhedra 2026-04-20T11:47:09Z Versionsgeschichte dieser Seite in de_evolutionary_art_org MediaWiki 1.27.4 http://de.evo-art.org/index.php?title=Counterchange_Patterns_and_Polyhedra&diff=4068&oldid=prev 2015-01-29T22:08:53Z

<p>Die Seite wurde neu angelegt: „ == Reference == B.G. Thomas: <a href="/index.php?title=Counterchange_Patterns_and_Polyhedra" title="Counterchange Patterns and Polyhedra">Counterchange Patterns and Polyhedra</a>. In: <a href="/index.php?title=Bridges_2009" title="Bridges 2009">Bridges 2009</a>. Pages 177–182 == DOI == == Abstract == Recent research has e…“</p> <p><b>Neue Seite</b></p><div><br /> == Reference ==<br /> B.G. Thomas: [[Counterchange Patterns and Polyhedra]]. In: [[Bridges 2009]]. Pages 177–182 <br /> <br /> == DOI ==<br /> <br /> == Abstract ==<br /> Recent research has examined the difficulties encountered when attempting to apply two-dimensional repeating<br /> designs to wrap around the surface of polyhedra. The study was concerned with symmetry in pattern but did not<br /> consider symmetries that involve a color change. A pattern is said to have color symmetry when it exhibits, as a<br /> minimum, one symmetry that is color-changing. Counterchange designs are produced when the color-changing<br /> symmetries of a pattern involve only two colors. This paper discusses the problems involved in the application of<br /> counterchange patterns to polyhedra, focusing particular attention on the icosahedron.<br /> <br /> == Extended Abstract ==<br /> <br /> == Bibtex == <br /> <br /> == Used References ==<br /> [1] B.G. Thomas and M.A. Hann, Patterned Polyhedra: Tiling the Platonic Solids, in R. Sarhangi and J.<br /> Barrallo (eds.) Bridges Donostia: Mathematical Connections in Art, Music, and Science, pp.195-202.<br /> 2007.<br /> <br /> [2] B.G. Thomas and M.A. Hann, Patterns in the Plane and Beyond: Symmetry in Two and Three<br /> Dimensions. Monograph no. 37 in the Ars Textrina series, The University of Leeds International<br /> Textiles Archive (ULITA). 2007.<br /> <br /> [3] B.G. Thomas and M.A. Hann, Patterning by Projection: Tiling the Dodecahedron and other Solids, in<br /> R. Sarhangi and C. Séquin (eds.) Bridges Leeuwarden: Mathematical Connections in Art, Music, and<br /> Science, pp.101-108. 2008.<br /> <br /> [4] D.K. Washburn and D.W. Crowe, Symmetries of Culture: Theory and Practice of Plane Pattern<br /> Analysis. Seattle, University of Washington Press, chapter 3. 1988.<br /> <br /> [5] I. Hargittai and M. Hargittai, Symmetry: A Unifying Concept, Bolinas, California, Shelter<br /> Publications, p.116. 1994.<br /> <br /> [6] E.H. Gombrich, The Sense of Order, Oxford, Phaidon Press Ltd. 1979.<br /> <br /> [7] H.J. Woods, The Geometrical Basis of Pattern Design. Part 4: Counterchange Symmetry in Plane<br /> Patterns, Journal of the Textile Institute, Transactions, 27, T305-T320. 1936.<br /> <br /> [8] M.A. Hann and G.M. Thomson, The Geometry of Regular Repeating Patterns, The Textile Institute,<br /> Manchester. 1992.<br /> <br /> [9] D. Schattschneider, Visions of Symmetry. Notebooks, Periodic Drawings and Related Works of M.C.<br /> Escher, New York, Freeman, p.100. 1990.<br /> <br /> [10] R.L.E. Schwarzenberger, Color Symmetry, Bulletin of the London Mathematical Society, 16, pp.<br /> 209-240. 1984.<br /> <br /> [11] D. Schattschneider, In Black and White: How to Create Perfectly Colored Symmetric Patterns,<br /> Comp. &amp; Maths. with Appls. 12B, 3/4, pp.673-695. 1986.<br /> <br /> [12] H.S.M. Coxeter, Colored Symmetry, in H.S.M. Coxeter et al. (eds.) M.C. Escher: Art and Science,<br /> Amsterdam and New York, Elsevier, pp.15-33. 1986.<br /> <br /> [13] N.V. Belov and T.N. Tarkhova, Dichromatic Plane Groups, in A.V. Shubnikov and N.V. Belov<br /> (eds.) Colored Symmetry, New York, Pergamon. 1964.<br /> <br /> <br /> == Links ==<br /> === Full Text === <br /> http://archive.bridgesmathart.org/2009/bridges2009-177.pdf<br /> <br /> [[intern file]]<br /> <br /> === Sonstige Links ===<br /> http://archive.bridgesmathart.org/2009/bridges2009-177.html</div>

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