The wizzle Seagull belongs to the pg symmetry group of the 17 wallpaper symmetry groups, which has glide-reflection in one direction but lacks reflection (Baloglou, 2007). The Seagull creates a periodic tessellation based on a square grid, thus possessing the trivial isometry of a 360° rotation as well as many trivial isometries of translation (horizontal, vertical, diagonal). In the above images, where you see the tessellation created by the Seagull, you can observe the isometries of horizontal translation and vertical glide-reflection. These isometries also constitute the elementary solving rule of the Seagull. A set of four tiles forms a meta-tlile, the basic structural unit of the infinitely repeating (with translation isometry) pattern that fills the Euclidean plane, providing a second approach to solving the Seagull.

For educational purposes, and not only, you can use the tiles of the Seagull to create all kinds of isometries (translation, reflection, glide-reflection, all types of rotations: 2-fold, 3-fold, 4-fold, 6-fold, etc., and compositions of isometries). However, not all of these isometries create a tessellation on the plane. You can find more details in the section "Wizzle in education".

Check out the solution of this wizzle.