7/28/2019 Islamic Geometric Ornament: The 12 Point Islamic Star. VI: 8 Plus 12 Point star. http://slidepdf.com/reader/full/islamic-geometric-ornament-the-12-point-islamic-star-vi-8-plus-12-point 1/9 Part VI: Twelve Point plus Eight Point Star Tiling Islamic Geometric Ornament: Construction of the Twelve Point Islamic Star The tilings of the twelve pointed Islamic star studied so far have been simple. The entire pattern was developed by extension of the parent 12 point star. The common and appealing historic pattern shown here is different. Still, it is not terribly complex. How are two perfect Islamic star patterns constructed to blend seamlessly? 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. VI: 8 Plus 12 Point star.
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7/28/2019 Islamic Geometric Ornament: The 12 Point Islamic Star. VI: 8 Plus 12 Point star.
The triangle defined by points (o12), (e) and (o8) contains an enormous
amount of information. This triangle is useful since distance (o12-e) is one
half of the repeat dimension of the pattern. This would be used to scale the
layout for a defined space.
Since the layout centered at (o8) defines an eight point star, we know thatangle (a o8 e) is 45° and that the blue layout inter-radius is its bisector. A
layout defined by bisecting these angles is simple.
Drawing a divided square and it diagonal is easy. The repeat spacing is
determined and a layout square is drawn. [See App. I] Points (o8), (o12)
and (e) are obvious. The angle at (o8) is easily bisected as shown. [See App. II]
The next step is not quite as obvious but is equally simple.
The three radii and inter-radii from (o12) trisect an angle.
Trisecting an angle exactly is not generally possible, but this
case, trisecting a 45 angle is exact and easy. This is one
eighth of a 24 fold divided circle, which has been
constructed here many times. It is not clear what size to
make the layout for this 24 fold division step, so size is
ignored for the moment. Any convenient size layout circle
is used. The usual two staggered hexagons are used to
divide the circle and the radii and inter-radii are drawn.
An interesting result is produced. Point (o’) is defined
without further effort. The point is defined uniquely by the
definition of the eight fold and twelve fold divisions of the
circle. No other information is needed
Several things are known now. Point (o’) lies on the tiling
edge of the dodecagon and octagon. It can define the
common side of the layout polygons.
The common side defines both the layout circle and octagon
for the eight fold star and both the layout circle and the
dodecagon for the twelve fold star.
Point (o’) on that shared side also defines the minor layout
circle. That circle has an equal radius, (o’ a) on both the
eight and twelve fold star.
The decision to make the eight fold star a parallel arm star
completely defines the pattern and the layout can be