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No. Objects can have reflective symmetry but no rotational symmetry.
This is the definition of "rotational symmetry", or if the statement is true for any number of degrees of rotation it is also "circular symmetry.".
Not exactly. Rotational symmetry means that a shape will look the same if the object is rotated around some axis, by ANY angle.There are no specific requirements as to where the axis must be.
Axial symmetry.