M.C. Escher's Hexagon Trick

In the applet below is a shape that tessellates the plane. That is to say, multiple copies of the shape--when rotated and pieced together--will fill the entire plane as far as you like in any direction.[br][br]This particular shape was created using M.C. Escher's "Hexagon Tessellation Trick". [br][br]Drag any of the red dots to explore M.C. Escher's "Hexagon Tessellation Trick." Different dots do different things. As you move the red dots, ask yourself:[br][br]What do you think is M.C. Escher's "Hexagon Tessellation Trick" for creating tessellating shapes?
Prompt 1
Can the 120 degree angles be changed?
Prompt 2
Do the big red dots do something different than the little red dots?
Prompt 3
Write a draft of the rules that govern M.C. Escher's "Hexagon Tessellation Trick".
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Information: M.C. Escher's Hexagon Trick