@article{Lu:2007:DQC,
optpostscript = {},
number = {5815},
month = feb,
author = {Peter J. Lu and Paul J. Steinhardt},
optkey = {},
optannote = {},
localfile = {papers/Lu.2007.DQC.pdf},
optkeywords = {},
doi = {http://dx.doi.org/10.1126/science.1135491},
optciteseer = {},
journal = {Science},
opturl = {},
volume = {315},
optwww = {},
title = {{D}ecagonal and {Q}uasi-{C}rystalline {T}ilings in {M}edieval
{I}slamic {A}rchitecture},
abstract = {The conventional view holds that girih (geometric
star-and-polygon, or strapwork) patterns in medieval Islamic
architecture were conceived by their designers as a network of
zigzagging lines, where the lines were drafted directly with a
straightedge and a compass. We show that by 1200 C.E. a conceptual
breakthrough occurred in which girih patterns were reconceived as
tessellations of a special set of equilateral polygons (``girih
tiles'') decorated with lines. These tiles enabled the creation of
increasingly complex periodic girih patterns, and by the 15th
century, the tessellation approach was combined with self-similar
transformations to construct nearly perfect quasi-crystalline
Penrose patterns, five centuries before their discovery in the
West.},
pages = {1106--1110},
year = {2007},
}
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