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Showing posts from July 10, 2006
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Here's a little play with pentagons, squares and triangles. There are a few ways to construct this pattern. I'll describe the process I used. I started with a

Start with a loop of four squares.
Add a pair of pentagons between the shared edges of the squares, this make a larger loop with a hole in the middle. The pentagons space the squares further apart.
Add triangles in between adjoining polygons (see pictures below). This process turns the loop inside-out. Because there are twelve polygons in the loop, there are twelve new triangles added. The triangles separately form two counter-clockwise loops whereas the original loop was clockwise. The combination of the angles results in a single counter-clockwise loop. The inside of the original loop is now on the outside of the new loop.





With a bit of play, I fit the large loops together into repeating pattern. I put the large squares into something related to triangular grid. (see the last picture…