Girih 10/3 Star Pattern

With our calculations in hand (see previous post, and below), it was not difficult to recreate the “A” scaffolding for this 10/3 star pattern using an SVG polyline shape.

Girih Tile
From Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture paper by Peter J. Lu and Paul J. Steinhardt

Here are the calculations:

Element ID | Coordinates
(pt1) 271.353, 61.8315
(pt2) 196.353, 7.341
(pt3) 103.647, 7.341
(pt4) 28.647, 61.8315
(pt5) 0, 150
(pt6) 28.647, 238.1685
(pt7) 103.647, 292.659
(pt8) 196.353, 292.659
(pt9) 271.353, 238.1685
(pt10) 300, 150

Note that the points on the circle are listed in anti-clockwise order.

This is pleasing enough.  One line of code to produce a complex pattern that never gets blurry even when you scale it up in browser isn’t too shabby.

Moreover, the absolute precision of the implementation of this design is rather satisfying — and would be difficult, I should think, to achieve manually.

Looking ahead, though, I see challenges in getting to stages (C) and (D).

The authors of the academic paper where I found this design refer to it as a “simple periodic girih patterns incorporating decagonal motifs [that] can be constructed using a ‘direct strapwork method’ with a straightedge and a compass.”

Not so simple too see right off the bat how to go from (A) end up with (D) with doing a hack SVG job..

 

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