Yes, the capital letter N has rotational symmetry but no lines of symmetry:
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The letters S, N, Z, for example.
It has line symmetry (straight down the center) but not rotational symmetry.
Yes. Any equilateral shape can have both rotational and line symmetry.
No A rectangle has rotational symmetry as well
parallelogram * * * * * A parallelogram does have rotational symmetry (order 2).