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Can a figure have two lines of symmetry and no rotational symmetry?

Can a figure have two lines of symmetry and no rotational symmetry?
 

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Sorry, neither ellipses nor rhombuses fit Rachel's criteria. These do indeed have rotational symmetry of order 2 -- a half turn will result in the same image.

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David T. | Experienced Math and Physics TutorExperienced Math and Physics Tutor
4.8 4.8 (12 lesson ratings) (12)
-1
Also a Rhombus. I turns out that Rhombus' can be closely related to the ellipses described above, and maybe shouldn't be seen as a truly separate phenomena:
 
inscribe a square in a circle. Pull two opposite corners of the square (and circle) outward or inward. The resulting figure is a rhombus inscribed in an ellipse.
 
In more than two dimensions this question can very interesting! But people are still getting PhD's describing these so I think it is not what you are asking about.
Justin S. | Math is my specialty!Math is my specialty!
4.9 4.9 (34 lesson ratings) (34)
-1
Yes! One example would be an ellipse. It has 2 lines of symmetry, one along the major axis and one along the minor axis, but it doesn't have rotational symmetry.