The wizzle Geo 9 belongs to the p3 symmetry group of the 17 wallpaper symmetry groups, which has 3-fold rotation (Baloglou, 2007). Geo 9 creates a periodic tessellation based on a hexagonal 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 Geo 9, you can observe the 3-fold rotation centers on three of the six grid nodes. These isometriy of 3-fold rotation also constitutew the elementary solving rule of Geo 9. A set of six tiles (three double 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 Geo 9.

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.