An ellipse has rotational symmetry of order 2.
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yes, in fact it can have 6 rotational symmetries.
None, however the semicircle has one folding axis of symmetry perpendicular to the midpoint of the straight side
The heart does have both symmetries. it can be split through the middle and rotated 4 times to make rotational symmetry
A parallelogram.A parallelogram.A parallelogram.A parallelogram.
For a star shaped figure, as many as the number of points. For a real star (like the ones up in the sky) either infinitely many or none - depending on the level of detail that you look at. The surface of any star has lots of dimples and bumps caused by stellar activity and these will break up any symmetry. If you ignore these fine details, then the star is a smooth ellipsoid and has infinitely many rotational symmetries. These symmetries are along the star's axis of rotation. For any other axis, the star's rotation will make the equatorial region bulge out and so there will be no symmetries.