Q: What Quadrilateral which has no lines of symmetry and rotational symmetry order 2?

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A square !

Triangle * * * * * The only triangle with rotational symmetry of order 3 is an equilateral triangle and that has 3 lines of symmetry, not 0. The triskelion (the three legs) on the Isle of Man flag has rotational symmetry of order 3 but no lines of symmetry.

A regular hexagon has 6 rotational symmetries (rotational symmetry of order six) and 6 reflective symmetries (six lines of symmetry).

Yes a rhombus has 2 lines of symmetry. These lines of symmetry join its opposite corners.

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Related questions

Parallelogram.

A rectangle.

parallegram

parallelogram * * * * * A parallelogram does have rotational symmetry (order 2).

no shape does! * * * * * Not true. A parallelogram has rotational symmetry of order 2, but no lines of symmetry.

A square !

A tetrad has rotational symmetry of order 4. It also has no lines of symmetry. It is also known as a swastica.

not possible

Not necessarily, except rotational symmetry of order 1.

Triangle * * * * * The only triangle with rotational symmetry of order 3 is an equilateral triangle and that has 3 lines of symmetry, not 0. The triskelion (the three legs) on the Isle of Man flag has rotational symmetry of order 3 but no lines of symmetry.

Assuming that qadrilateal is meant to be quadrilateral then the answer is that in general it would have rotational symmetry of order 1.

Yes. A circle has infinitely many lines of symmetry and it also has rotational symmetry of infinite order.