Kürschák's Tile
A beautiful construction by Josef Kurschak, connected to his visual proof that the area of the this dodecagon is 3 times the circumradius.
What questions does it raise?
Read about the tile at MathWorld:
http://mathworld.wolfram.com/KurschaksTile.html
Read about Kurschak at Wikipedia:
http://en.wikipedia.org/wiki/J%C3%B3zsef_K%C3%BCrsch%C3%A1k