http://de.evo-art.org/index.php?action=history&feed=atom&title=Patterned_Polyhedra%3A_Tiling_the_Platonic_Solids 2026-05-27T14:06:28Z Versionsgeschichte dieser Seite in de_evolutionary_art_org MediaWiki 1.27.4 http://de.evo-art.org/index.php?title=Patterned_Polyhedra:_Tiling_the_Platonic_Solids&diff=4134&oldid=prev 2015-01-30T19:13:03Z

<p>Die Seite wurde neu angelegt: „ == Reference == B.G. Thomas and M.A. Hann: <a href="/index.php?title=Patterned_Polyhedra:_Tiling_the_Platonic_Solids" title="Patterned Polyhedra: Tiling the Platonic Solids">Patterned Polyhedra: Tiling the Platonic Solids</a>. In: <a href="/index.php?title=Bridges_2007" title="Bridges 2007">Bridges 2007</a>. Pages 195–202 == DOI == == Abstrac…“</p> <p><b>Neue Seite</b></p><div><br /> <br /> == Reference ==<br /> B.G. Thomas and M.A. Hann: [[Patterned Polyhedra: Tiling the Platonic Solids]]. In: [[Bridges 2007]]. Pages 195–202 <br /> <br /> == DOI ==<br /> <br /> == Abstract ==<br /> This paper examines a range of geometric concepts of importance to the further understanding of two- and three-<br /> dimensional design. A brief explanation is given of symmetry in patterns and tilings, and attention is focused on a<br /> particular set of polyhedra, known as the Platonic solids. The difficulties encountered in attempting to apply two-<br /> dimensional repeating designs to regular polyhedra, avoiding gap and overlap and ensuring precise registration, are<br /> recognized. The results of ongoing research at the University of Leeds are presented. The symmetry characteristics<br /> of importance to the process are identified, and the patterning of each of the five solids is explained and illustrated.<br /> Avenues for further research are suggested.<br /> <br /> == Extended Abstract ==<br /> <br /> == Bibtex == <br /> <br /> == Used References ==<br /> [1] H.S.M. Coxeter. Regular Polytopes. London, Methuen, p.iv. 1948.<br /> <br /> [2] H. Weyl. Symmetry. Princeton, Princeton University Press. 1952.<br /> <br /> [3] H.S.M. Coxeter. Introduction to Geometry. New York, John Wiley and Sons. 1969.<br /> <br /> [4] G.E. Martin. Transformation Geometry: An Introduction To Symmetry. Springer-Verlag, New York.<br /> 1982.<br /> <br /> [5] H. J. Woods, The Geometrical Basis of Pattern Design. Part 3: Geometrical Symmetry in Plane<br /> Patterns, Journal of the Textile Institute, Transactions, Vol. 26, T341-T357. 1935.<br /> <br /> [6] D. Schattschneider. Plane Symmetry Groups: Their Recognition and Notation, American<br /> Mathematical Monthly, 85, 6, pp.439-450. 1978.<br /> <br /> [7] P.S. Stevens. Handbook Of Regular Patterns: An Introduction To Symmetry In Two Dimensions.<br /> Cambridge, Mass, MIT Press. 1984.<br /> <br /> [8] D.K. Washburn and D.W. Crowe. Symmetries of Culture: Theory and Practice of Plane Pattern<br /> Analysis. Seattle, University of Washington Press. 1988.<br /> <br /> [9] M.A. Hann and G.M. Thomson. The Geometry of Regular Repeating Patterns. Manchester, The<br /> Textile Institute. 1992.<br /> <br /> [10] K. Critchlow. Order in Space: A Design Sourcebook. New York, Thames and Hudson. 1969.<br /> <br /> [11] P. Pearce. Structure In Nature Is A Strategy For Design. Cambridge, Mass, MIT Press. 1978.<br /> <br /> [12] H. Cundy and A. Rollett. Mathematical Models. Norfolk, Tarquin Publications. 3rd ed. 1989.<br /> <br /> [13] A. Holden. Shapes, Space and Symmetry. Dover, New York. 1991.<br /> <br /> [14] P.R. Cromwell. Polyhedra. New York, Cambridge University Press. 1999.<br /> <br /> [15] P. Tantiwong. The Application of Symmetry Concepts to Regular Repeating Pattern Design. Ph.D.<br /> Thesis, De Montfort University, p.27. 2000.<br /> <br /> [16] D. Schattschneider and W. Walker. M.C. Escher Kaleidocycles. Norfolk, Tarquin Publications. 3rd<br /> ed., p.26. 1982.<br /> <br /> [17] G.S. Pawley. Plane Groups on Polyhedra, Acta Crystallographica, 15, pp.49-53. 1962.<br /> <br /> <br /> == Links ==<br /> === Full Text === <br /> http://archive.bridgesmathart.org/2007/bridges2007-195.pdf<br /> <br /> [[intern file]]<br /> <br /> === Sonstige Links ===<br /> http://archive.bridgesmathart.org/2007/bridges2007-195.html</div>

Gbachelier