7/28/2019 Islamic Geometric Ornament: The 12 Point Islamic Star. VII: 9 Plus 12 Point Star Tiling http://slidepdf.com/reader/full/islamic-geometric-ornament-the-12-point-islamic-star-vii-9-plus-12-point 1/7 Part VII: Twelve Point plus Nine Point Star Tiling Islamic Geometric Ornament: Construction of the Twelve Point Islamic Star The figure above is a particularly fascinating case of a pattern which should be very complex, but is in fact very simple. It contains the nine point Islamic star. There is no exact compass and straight edge construction of a nine sided polygon, as there is no exact compass and straight edge trisection of an angle. Yet, the figure above is constructed easily by compass and straight edge rules. This is also the first case of an arbitrarily, but precisely, spaced tiling which is presented here. Alan D Adams, Holland, New York, 6 June 2013. License: Creative Commons -Attribution 3.0 Unported (CC BY 3.0) Text, photos and drawings.
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Islamic Geometric Ornament: The 12 Point Islamic Star. VII: 9 Plus 12 Point Star Tiling
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7/28/2019 Islamic Geometric Ornament: The 12 Point Islamic Star. VII: 9 Plus 12 Point Star Tiling
The decision to set the smaller, nine point, star as a parallel arm star determines the layout of the 12 point star.
As dissimilar stars, the 12 point star must be tapered if the 9 point is chosen as parallel. Extending the arm endof the nine point star to intersect the minor layout circle bisector sets the 12 point star layout.
Three layout circles are required for the 12 point star since it is a tapered star. The layout circles are transferred
to the three 12 point layouts and the star is drawn in as usual. The only issue left to determine is how the
remaining arm ends extend out to terminate. In this case, the strict rules based extensions result in entirely
satisfactory results. All decisions in this layout protocol are directed at maintaining the best possible symmetry
for the minor elements, and this minor five point star shows very pleasing symmetry.
7/28/2019 Islamic Geometric Ornament: The 12 Point Islamic Star. VII: 9 Plus 12 Point Star Tiling
6) See a Nasrid ceiling panel in the Aga Khan collection, 14-15th CE. Access Nr AKM00730
See David Wade’s http://www.patterninislamicart.com - images SPA1003, SPA1008, SPA1542x from the Alhambra. Most of theAlhambra examples are modifications with parallel arms for both nine and 12 point stars. See also Wade’s SPA1821 for another variant.
In addition, www.tilingsearch.org reports this pattern as occurring in the Alhambra in several places. Their index: T01161, data160/
J43C.
“Two adjacent mosaic panels in each of the four corners of the Mirador de Lindaraja.... window grilles round the lantern of the Sala delos Abencerrajes; as a wooden ceiling over the north part of the Sala del Mexuar; and as the middle of three window grilles over thearch linking the Patio de los Arrayanes and the Sala de la Barca.”
Examples are found with most possible combinations of tapered and parallel arm layouts;A ceiling of the Sultan Oljaytu Mausoleum, Ilkhanid Iran 14th cent. Wade’s image IRA2701;Parallel arm 12 Point star, reversed taper nine point star- The doors at the Khanqah of Baybars al-Gashaqkir, Mamluk Cairo. AH 709;A double tapered Mughal example is Wade’s image IND0729 from the Masjid Jami, Fatehpur Sikri.
7) Polygons with 3, 4, 5, 6, 8, 10, 12, 15, 16 or 17 sides, or even multiples of these, are constructible with compass and straight edge.Others are approximations. The regular 17 sided polygon construction was only published in the 19th century.
8) For a variation with taper arms in both nine and twelve point stars, see; B. Lynn Bodner, A Nine- and Twelve-Pointed Star PolygonDesign of the Tashkent Scrolls, Bridges, 2011, 147-154. Bodner uses a very different approach to pattern construction to generate adifferent approximate construction.