Sunday, February 18, 2024

Tiling Stars

Red stars, triangles, and kites arranged into nine-fold and six-fold arrays.
One of my hobbies is playing around with different types of tilings.  Mostly I like to play around with Penrose Kites and Darts.  I also like to try to fit stars into regular patterns.  The most recent exploration that I've done comes from Daud Sutton's "Islamic Design," where he talks about making a grid out of right triangles, and then placing regular polygons and other shapes onto the edges and corners of the triangles.  In the case that I was interested in, he used five-pointed stars.  

Getting the stars down on the triangles was simple enough, but it took me a lot of wiggling to get the nine kite-shapes at the top and bottom of the design to look symmetric and not smooshed.

I'll have to see what sorts of patterns will result from right-triangles which form squares instead of hexagons.

A couple of weeks ago, I read about a technique for putting odd-numbered polygons and stars together.  Start with a figure, duplicate and reflect it, then make the two closest points touch.  Skip a point on ether side of the touching point, and place a reflected duplicate there, too.  This will make a repeating line, which you can put together into a mesh.  I tried it with 5-, 7-, and 9-stars; the 7-stars were the most aesthetic, so I put together some interwoven 7-stars into a larger interwoven pattern.

Whats fun about this technique is that it allows one to break away from patterns that are hexagon- or square-based. 

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