Decorating Regular Polyhedra Using Historical Interlocking Star Polygonal Patterns — A Mathematics and Art Case Study

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Reference

Reza Sarhangi: Decorating Regular Polyhedra Using Historical Interlocking Star Polygonal Patterns — A Mathematics and Art Case Study. In: Bridges 2014. Pages 243–252

DOI

Abstract

This paper reports on the application of some historical interlocking patterns for the embellishment of the regular polyhedra (Platonic and Kepler-Poinsot solids). Such patterning can be extended to cover surfaces of some other convex and non-convex solids. In this regard, first the Shamseh n/k star polygon method and the radial grid method will be employed, and step-by-step geometric constructions will be demonstrated, then the girih tile modularity method will be used to explore more patterning designs. Then, the girih tile modularity is used to explore more patterning designs.

Extended Abstract

Bibtex

Used References

[1] Bourgoin, J., Arabic Geometrical Pattern & Design, Dover Publications, Inc., New York, 1973.

[2] Bridges Mathematical Art Exhibitions: http://bridgesmathart.org/bridges-galleries/art-exhibits, 2014.

[3] Hart, G.W., http://www.georgehart.com/virtual-polyhedra/vp.html,1996.

[4] Lu, P.J. & Steinhardt, P.J., Decagonal and quasi-crystalline ..., Science 315, 2007, pp. 1106-1110.

[5] Maheronnaqsh, M., Design and Execution in Persian Ceramics, Abbasi Museum Press, Tehran, 1984.

[6] Meenan E.B. and Thomas B.G., Escher-type Tessellations and Pull-up Polyhedra: Creative Learning for the Classroom, Bridges Pécs Conference Proceedings, Hungary, 2010, pp 539-544.

[7] Necipoğlu, G., The Topkapi Scroll: ..., Getty Center Publication, Santa Monica, USA, 1995.

[8] Sarhangi R., Interlocking Star Polygons ..., Nexus Network Journal, Springer, 2012, pp. 345-372.

[9] Sarhangi, R. and Séquin, C. H. (Editors), Bridges Conference Proceedings, Winfield, Kansas, 2004.

[10] Thomas B.G. and Hann M.A., Patterning by Projection: Tiling the Dodecahedron and other Solids, Bridges Leeuwarden Proceedings, the Netherlands, 2008, pp. 101-108.

[11] Wenninger M., Polyhedron Models, Cambridge University Press, 1974, pp. 41-42.


Links

Full Text

http://archive.bridgesmathart.org/2014/bridges2014-243.pdf

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Sonstige Links

http://archive.bridgesmathart.org/2014/bridges2014-243.html