Rotational symmetry (4-fold)

A polyomino has four-fold rotational symmetry if it is identical to its 90˚ rotation. If a polyomino has this type of symmetry, also has two-fold rotational symmetry, since a 180˚ rotation is equal to two 90˚ rotations. This type of symmetry is represented by $C_4$, the cyclic group of order 4.

The smallest polyomino with this symmetry is the "windmill" polyomino below. This type of symmetry is possible for octominoes and for polyominoes of size $4k$ and $4k+1$ for $k \gt 2$.

Polyomino list