Triangle: The other shapes have an even number of sides.
Square: The numbers of sides on the other two is divisible by 3
Hexagon: For sides of a fixed length, the other two shapes are rigid structures (the square can distort to a rhombus but then it is no longer a square.)
or
Triangle: It can have all acute angles.
Square: It can (must ) have all right angles.
Hexagon: It can have all obtuse angles.
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