Islamic Geometric Ornament: The 12 Point Islamic Star. 4: Alternate TIlings, Square Repeats

7/30/2019 Islamic Geometric Ornament: The 12 Point Islamic Star. 4: Alternate TIlings, Square Repeats.

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Part IV: Alternate Tilings, Square Repeats.

Islamic Geometric Ornament:

Construction of the Twelve Point Islamic Star

Many alternate Tilings exist for the classic parallel arm 12 point Islamic star. One of the simplest is a square

repeat. The 12 point star has fourfold symmetry as well as sixfold. Stars are still tiled tip to tip in the figure

above, but now in a square pattern. Exactly the same rules apply.

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



In this figure, the four red arms of the 12 point star defined the symmetry of the tiling figure, a square. Layout

for the twelve point star uses exactly the same divided circle. The same major layout circle is inscribed in the

tiling figure, now a square. The same two layout hexagons were constructed in the tiling figure.

Exactly the same minor layout circle is used to define the arms of the star. It is located, as before, on the inter-

radius at the tiling polygon. The same rule is used to extend the ends of the arms. Where an arm end does not

intersect the tiling polygon at the end of the arm, it is extended out until it intersects.

The resulting figures are very similar. The star itself is identical. The half five point star in yellow, shared in

the tiling, is identical. The remaining elements are altered. The corner polygon, in yellow, is slightly altered. It

will become a irregular hexagon in the hexagonal tiling, it will become an irregular octagon in the square tiling.

Three completely new figures are created in the square tiling, in orange. This is a general feature of tiling

polygons which expand outward beyond the ends of the star arms. The new space inside the tiling polygon

needs to be filled while following the rules of pattern construction. New elements will appear in the tiling and

the challenge is to control the layout to make these elements pleasing in size and symmetry. The effect of the

retiling is subtle but important in this parallel arm star.



The two linear bands above are the tiling of the hexagonal layout, with three full and eight partial tiles- and the

tiling of the square layout, with three full tiles. With the subtle difference in layout, the bottom band might have

been called a “tweaked,” or an arbitrarily modified band of the hexagonal tile. It is not. It is retiled by specific

rules.

The square tiling also offers new options for emphasis. The new elements formed in the tiling are balanced

elements which can be used to good effect in the some figures. The bands above emphasize the new elements

formed in the tiling with strong color contrast. Greater or lesser emphasis can be added in applications where a

color contrast can be used. This subject will be dealt with very little here, but it can change the impression of a

pattern dramatically.



The area to be decorated is frequently defined by other issues. A pattern figure needs to be fit to a space. The

two fields below return to the larger tilings, where the properties of the parent star dominate. They show very

similar size major stars. Each shows the preferred quarter pattern in the corners. This shows that the new

symmetry elements introduced by the square tiling may also cause problems.

In this case, the top figure of hexagonal tiling shows a clean horizontal axis and a nice division of the panel into

three visual fields, each containing a major star.

In the field of the square tiling, on the bottom, the new square element in the field is not in harmony with the

dominant 12 fold star symmetry or the proportions of the space. The central square figure draws the eye

strongly but adds little to the figure. The star could be moved to the center, but this gives even poorer results.

This square tiling might not be the best choice for this field.

The best tiling for a particular size field is very hard to predict in advance. It will depend on the proportions of

the field to be covered and it may depend on other patterns in a larger composition. It is fortunate that there are

several possibilities.



The square tiling polygon still fits very tightly around the major star. There are few other options for alternate

figures with a parallel arm star. An alternate lacing of the figure, the same lacing which was discussed above in

the hexagonal tiling polygon, can be used here.

The same rules used in the hexagonal case are used. The arm layout lines are extended to intersect the tiling

polygon. To define the ends of the arms, a new minor layout circle is drawn where that layout line intersects the

tiling square. Two circles are needed, drawn in red, to transfer the two points to the remaining radii and inter-

radii. The arm ends are drawn in by connecting the two new layout circles.

Where they do not intersect the tiling polygon, the arm ends are continued to intersect at the point marked in

red. The layout is complete, and a very interesting figure results.

This lacing strongly emphasizes the four fold symmetry of the pattern and creates a set of new figures with their

own strong fourfold symmetry.



This lacing decreases the emphasis on the 12 fold major star dramatically. It is much more successful as a

square tiling, at the price of a lower rotational symmetry major star.

Tapered arm stars can be constructed with the square tiling but the problem with conflict of 12 fold major star

and the fourfold symmetry elements is only aggravated. While the figure above is seen in historic figures,

square tilings of the isolated star are not common. Square tiling is more common in stars with expanded tiling

polygons, where a buffer can exist between the major star and its neighbors; this is the next facet to explore.

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Islamic Geometric Ornament: The 12 Point Islamic Star. 4: Alternate TIlings, Square Repeats