The wizzle Geo 2 belongs to the p4 symmetry group of the 17 wallpaper symmetry groups which has centers of 4-fold rotations (90°) and distinct centers of 2-fold rotations (180°)  (Baloglou, 2007). Geo 2 creates a periodic tessellation based on a square grid, thus possessing the trivial isometry of 360° as well as many trivial isometries of translation (horizontal, vertical, diagonal). In the above images, depicting the tessellation created by Geo 2, you can observe the centers 4-fold and 2-fold rotations in the nodes of the square grid. These isometries constitute the elementary solving rule of Geo 2. A set of 4 tiles forms a metatile, the basic structural unit of the infinitely repeating (with translation isometry) pattern, filling the Euclidean plane and providing a second approach to solving Geo 2.

For educational purposes, and not only, you can use the tiles of the Geo 2 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".

Δείτε τη λύση του wizzle.