We were at the Pennsylvania National Quilt Extravaganza last weekend. I regret I didn't get the name of the man who made this one.
It bore close inspection. I thought at first that it was made of equilateral triangles—that's the usual way to make a pattern of repeating hexagons like this. But I realized it's actually made of 30-60-90 triangles.
The quilter has taken different _striped_ fabrics, and cut twelve pieces of each. Then he joins them in pairs so that the stripes make a right angle in each pair, which forms an equilateral triangle. Then he joins six triangles, each with its right-angled stripes, into a hexagon.
And then he carefully matches the hexagons so that the half-square in each part makes sense with the half-squares in the adjoining hexagons.