No.
For example, a hexagon with equal angles and sides of lengths a,b,a,b,a,b has rotational symmetry of order 3, but it has no reflection symmetry.
No.
For example, a hexagon with equal angles and sides of lengths a,b,a,b,a,b has rotational symmetry of order 3, but it has no reflection symmetry.
No.
For example, a hexagon with equal angles and sides of lengths a,b,a,b,a,b has rotational symmetry of order 3, but it has no reflection symmetry.
No.
For example, a hexagon with equal angles and sides of lengths a,b,a,b,a,b has rotational symmetry of order 3, but it has no reflection symmetry.