Islamic Geometric Ornament: The 12 Point Islamic Star. 5: Blue Mosque of Aqsunqur

7/30/2019 Islamic Geometric Ornament: The 12 Point Islamic Star. 5: Blue Mosque of Aqsunqur

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Part V: the Blue Mosque of Aqsunqur.

Islamic Geometric Ornament:

Construction of the Twelve Point Islamic Star

The extended layouts of this star do not yet lead back to the original chapter head figure of part V, but the path

is the same. An additional order of petals can be added to the star; the tiling hexagon can be moved one more

time outward to generate a new family of star layouts.

This figure differs from the figures studied so far and deserves special comment. This star interlaces with the

tiled neighbor stars and polygons without meeting at a point. It is not at first clear what should be defined as a

“tile” here. The unit defined as the “Unit Tile” should not overlap in the creation of the figure. A tile containing

the complete fourth order star as one would normally define it will not work. An infinite tiling polygon which

defines the pattern completely does exist here, but it is not as obvious as previous examples.

The construction of the answer is surprisingly simple. The previous examples of an expanded tiling hexagon

was drawn by constructing the circumscribed hexagon, rotated 15 degrees, on the original simple star layout.

This is exactly the same extension applied again.

Alan D Adams, Holland, New York, March 2013. License: Creative Commons -Attribution 3.0 Unported (CC BY 3.0) Text, photos and drawings.



The tiling hexagon which contains a unique repeating unit is obvious, as soon as it is recognized. All of the

rules required to construct this are already defined. About 90% of the layout is identical to the previous layout.

The initial layout is identical to the layouts already presented. The orientation of the tiling hexagon is chosen

and it is constructed as before. In this case, the 24 fold division of the circle is needed very early in the

construction to locate the 15° rotation of the star layout.

An additional layout hexagon is needed, drawn in red. This should be drawn very lightly since it will not be

used after this initial division. The circle is divided as before with 12 radii and 12 inter-radii. The outer circle

and red layout hexagon will not be show after this figure. They have served their purpose. Two further



hexagons are constructed. The first serves one purpose, as a spacer to move the star layout inward. It is

constructed on the first inter-radius past the vertex of the tiling hexagon; the new hexagon vertex lies on the

edge of the tiling hexagon; it is rotated 15° relative to the tiling hexagon.

A second hexagon, the hexagon which defines the major layout circle of the star, is constructed inside the

spacing hexagon on the next radius. It is rotated 30° relative to the tiling hexagon, aligned with parallel edges.

The major layout circle is inscribed in this inner hexagon. Note that these hexagons do not need layout circles

since the circle is already divided. They can be constructed by simply connecting the intersections on the radii.

The next few steps could be done exactly the same as the classic parallel arm star. Several are not needed. The

two layout hexagons in the standard layout are drawn to divide the circle. This was already done early in this

layout. They are drawn in grey here to keep the appearance the same as the standard layout. The point (a), the

end of the star arms, lies on the major layout circle by definition. This layout shows the most general definition

of the location of the minor layout circle, which defines the arm shape and taper. This lies on the line through

(a) perpendicular to the radius which defines point (a). Point (o’) lies on the next inter-radius.

The layout of the star arm proceeds exactly as for the classic parallel arm star to define points (b) and (c).



Circles are drawn in to transfer points (b) and (c) around the layout. Points (b) on the inter-radii and points (c)

on the radii are connected to give the basic star polygon. These sides are extended out to intersect the layout

dodecagon, in light blue, and inward to intersect.

This is a parallel arm star, and the ends of the arm follow the layout dodecagon. At this point, if the two grey

hexagons are drawn back in in blue, the layout is exactly the same as the classic parallel arm star with two

rotated layout hexagons spaced out by rotations beyond the original tiling hexagon.

The first departure from the classic layout is the extension of the arm ends. In this star, they extend until the

intersections define a third and fourth order of petals around the basic star. This also causes a problem. Some

of these intersections are outside the tiling hexagon. This is not allowed by tiling rules. The solution was

already introduced above. If a line continues in a straight line past a tiling edge, it must re-enter the tiling edge

at the same angle and opposite direction.



The general construction of this is long, but again, a shortcut can be used. The intersections to be moved lie on

radii perpendicular to the tiling edge. Moving the point to an equal distance inside the tiling edge gives the

correct construction. This is easy. Two points equidistant from point (x) on a line lie on a circle around (x).

The layout circle, drawn as on the right above, defines two new layout circles to transfer the layout to all 12

arms of the star. Only six arms extend beyond the tiling hexagon but the best possible symmetry requires

performing the same operation on all twelve arms. The second, outer, layout circle is required to identify the

indicated points.

Completing the layout and cleaning up the figure leads to the completed figure on the right. Four hexagons and

six layout circles will be required for each repeat of this figure. The rules were followed, it should tile perfectly



What appears to be a very complex figure with independent interlaced polygons and complex interlacing of the

major star is a simple rules based extension of the classic star. This layout reproduces the proportions of the 8th

century AH marble panel from the Mameluke mosque of Aqsunqur exactly.5

As for the other hexagonal layouts, this figure can be tiled as a square repeat with very small changes and minor

layout additions. The two figures above use the same layout change and a different lace. Exactly as for the

previous examples, layout lines are extended across the void in the square tiling polygon until they intersect. In

this case, the result is still too sparse. A new layout element is introduced, the layout circle at the corner of the



tiling polygon, defined by the indicated point. In the first case, very similar to the square tiling of the third

order star, this layout circle defines an octagonal lacing. In the second, it defines an interlaced square which

balances the areas of the minor figures. Both of these solutions are quite common in historic patterns.

The tilings shown so far have been very simple. They use a single unit tile and no additional or very little

additional layout is added when that unit is tiled. Tilings do not need to be so simple. The next case will look a

a complex tiling which combines 12 and 8 point Islamic stars in a continuous interlacing pattern.

References:

5) Photos of the panel from the mosque of Aqsunqur (747 AH, 1347 CE) are found on David Wade’s site:

http://www.patterninislamicart.comas photos EGY1621 and EGY1620.

http://www.patterninislamicart.com/

http://www.patterninislamicart.com/

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Islamic Geometric Ornament: The 12 Point Islamic Star. 5: Blue Mosque of Aqsunqur