A three-blade ceiling fan has rotational symmetry of order 3. This means it looks the same after a rotation of 120° (360°/3). A plane of symmetry is an imaginary plane that divides the object into two mirror-image halves. For a three-blade fan, any plane that cuts through the center and a blade would not create identical halves because the opposite side would have a gap between blades. Therefore, it has no planes of symmetry.

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