Dissect a triangle into six smaller triangles (from midpoint of each side to centroid and from each vertex to centroid). Then rotate one pair of triangles apart to join adjacent sides. Now rotate the entire halves together (and perhaps beyond) to get a trapezoid (and then, I suppose a strange pentagon). The works here are the trails left by those rotating triangles. See the animation after the jump to get a feel for how the images came to be.

2014-08-17_unfolding_triangles.ggb |