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Yes. An ellipse (oval) has two lines of symmetry, but not a rotational symmetry. A parabola has one line and no rotation.
with corners: rectangles and rhombiwithout corners: ovals (ellipse)The diagonals are the two lines of symmetry of any rhombus that is not a square.
4 Lines of symmetry
2 lines OF SYMMETRY
There is no such thing as 8 lines of symmetry. A circle, for example, has infinitely many lines of symmetry.