Yes. An ellipse (oval) has two lines of symmetry, but not a rotational symmetry. A parabola has one line and no rotation.
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The letters H and Z have both line symmetry and rotational symmetry
F has no symetry : line or rotational symmetry
An equilateral triangle has both line symmetry and rotational symmetry. A non-equilateral isosceles triangle has line symmetry but not rotational symmetry. A scalene triangle has neither kind of symmetry.
A sphere has rotational symmetry of an infinite degree.