The wizzle Lama belongs to the p4 symmetry group of the 17 wallpaper symmetry groups, which has 4-fold and 2-fold rotations (Baloglou, 2007). Lama 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 Lama, you can observe the isometries of 4-fold and 2-fold rotations. These isometries also constitute the elementary solving rule of Lama. 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 Lama.

For educational purposes, and not only, you can use the tiles of the Lama 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, these isometries do not create a tessellation in the plane. You can find more details in the section "The wizzle as an educational tool."

Check out the solution of this wizzle.