A Parallelogram, a Diamond and a rhombus all have rotational symetry of two.
Others
Kite 1
Trapezium 1
Square 4
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Oh, dude, an oval has an infinite number of lines of symmetry, so technically it has infinite rotational symmetry. But like, who's really gonna sit there and rotate an oval forever just to prove a point, right? So, yeah, infinite rotational symmetry for the win!
two-fold
Oh, what a happy little question! A kite does indeed have rotational symmetry. Just like how you can turn a kite and it still looks the same, it has rotational symmetry. Keep exploring and creating, my friend!
There are no lines of symmetry.
An ellipse has two lines of mirror symmetry: the line that includes the two foci of the ellipse and the perpendicular bisector of the segment of that line between the two foci.