Hinged squares
Drag B and focus at special angles of the rhombus at B.
What kind of tiling do you get when the angle of the rhombus is 0˚ or 180˚?
What if the angle of the rhombus is 90˚?
What kind of tiling do you get when the angle of the rhombus is 60˚ or 120˚?
For this angle imagine each rhombus subdivided into two equilateral triangles.