Making the Tricorn Tessellation
First we made a triangular grid. It was accomplished by drawing circles. We began with a circle centered at point A above. We then drew a circle of the same size around B, a point on the circle, passing through point A. The intersections of these two circles created other centers from which to draw more circles. Those intersections made a grid of triangles (an isometric grid).
In the second figure, you can see that we drew triangle HJK and circles at L and M, stretching through points H and K respectively. Note carefully which points were used to make the triangle.
We got rid of the parts of circles L and M and kept arcs that wove in and out of the side HK meeting at its midpoint. One arc is just a 180 degree rotation of the other about the midpoint.
We got rid of the original triangle, and losing the dots in the grid would add to the 'mystery' of the construction. But first, we begin to cover the plane with copies of the tricorn (three-horned) HJK that fit perfectly together. A tessellation abhors negative space. Within some tricorns your design could display small triangles, hexagons or hex stars (yes, this is where you take over).
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