rectangle has inversion (180 deg rotation)
hexagon has 60 deg ratation, cyclic group genterated is
60, 120, 180, 240, 300, 360=0
equilateral triangle has 120 deg rotation, cyclic group genterated is
120, 240, 360=0
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For example the triskelion (the three legs) on the Isle of Man flag.
A Parallelogram, a Diamond and a rhombus all have rotational symetry of two. Others Kite 1 Trapezium 1 Square 4
A trapezium, a kite, an arrowhead, a quadrilateral with 4 different sides. In fact, anything other than a parallelogram (and its special cases).
Equilateral triangles have rotational symmetry.
none shapes have 1 rotational symmetry because in rotational symmetry one is none