http://de.evo-art.org/index.php?action=history&feed=atom&title=Concave_HexagonsConcave Hexagons - Versionsgeschichte2026-04-20T16:58:36ZVersionsgeschichte dieser Seite in de_evolutionary_art_orgMediaWiki 1.27.4http://de.evo-art.org/index.php?title=Concave_Hexagons&diff=4072&oldid=prevGbachelier: Die Seite wurde neu angelegt: „ == Reference == Paul Gailiunas: Concave Hexagons. In: Bridges 2009. Pages 243–250 == DOI == == Abstract == The tilings (n.3.n.3) exist in the sp…“2015-01-29T22:17:22Z<p>Die Seite wurde neu angelegt: „ == Reference == Paul Gailiunas: <a href="/index.php?title=Concave_Hexagons" title="Concave Hexagons">Concave Hexagons</a>. In: <a href="/index.php?title=Bridges_2009" title="Bridges 2009">Bridges 2009</a>. Pages 243–250 == DOI == == Abstract == The tilings (n.3.n.3) exist in the sp…“</p>
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== Reference ==<br />
Paul Gailiunas: [[Concave Hexagons]]. In: [[Bridges 2009]]. Pages 243–250 <br />
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== DOI ==<br />
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== Abstract ==<br />
The tilings (n.3.n.3) exist in the spherical, Euclidean or hyperbolic plane, depending on whether n is less than,<br />
equal to, or greater than 6. In all cases the dual tiling consists of rhombi, which can be taken in pairs to form<br />
"regular" concave hexagons. In the case of the spherical examples the tilings can be illustrated by colouring the<br />
faces of rhombic polyhedra. In the Euclidean plane "regular" concave hexagons allow tilings that cannot be<br />
constructed from the dual (6.3.6.3) tiling, some of which allow analogous tilings of non-"regular" concave<br />
hexagons. Some Escher-like designs are derived from such tilings.<br />
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Some of the possibilities in the hyperbolic plane are briefly considered.<br />
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== Extended Abstract ==<br />
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== Bibtex == <br />
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== Used References ==<br />
[1] P.Gailiunas, A Polyhedral Byway. Bridges Proceedings 2001, pp.115-122.<br />
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[2] S.T.Coffin, The Puzzling World of Polyhedral Dissections, OUP, 1990, pp.126−7.<br />
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[3] P.Gailiunas, Spiral Tilings. Bridges Proceedings 2000, pp.133-140, available online at http://www.mi.sanu.ac.yu/vismath/gal/index.html<br />
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[4] D.Schattschneider, Visions of Symmetry, W.H.Freeman and Company, 1990.<br />
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[5] P.Gailiunas, Some Monohedral Tilings Derived from Regular Polygons, Bridges Donostia Proceedings 2007, p.11.<br />
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[6] http://www.bridgesmathart.org/art-exhibits/bridges2007/gailiunas.html<br />
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[7] D.Dunham, 168 Butterflies on a Polyhedron of Genus 3, Bridges Proceedings 2002, pp.197-204.<br />
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[8] Grünbaum and Shephard, Tilings and Patterns, W.H.Freeman and Company, 1987, p.289.<br />
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[9] http://www.mi.sanu.ac.yu/vismath/gailiunas2008/index.html<br />
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== Links ==<br />
=== Full Text === <br />
http://archive.bridgesmathart.org/2009/bridges2009-243.pdf<br />
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[[intern file]]<br />
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=== Sonstige Links ===<br />
http://archive.bridgesmathart.org/2009/bridges2009-243.html</div>Gbachelier