The Geo 3 wizzle belongs to the p3 symmetry group of the  17 wallpaper symmetry groups, which only the isometry of 3-fold rotation (120°) (Baloglou, 2007).Geo 3 creates a periodic tessellation based on a hexagonal grid thus possessing the trivial isometry of 360° as well as many trivial isometries of translation (horizontal, vertical, diagonal). In the above images, where you see the tessellation created by Geo 3, you can observe the centers of 3-fold rotation at three of the six nodes of the initial hexagonal grid. This 3-fold rotation symmetry also constitutes the elementary solving rule of Geo 3. A set of three tiles assembled in three different ways, i.e., around the three different centers of 3-fold rotation, forms a metatile, the basic structural unit of the infinitely repeating (with translation isometry) pattern that fills the Euclidean plane, presenting a second approach to solving Geo 3.

For educational purposes, and not only, you can use the tiles of the El Drago 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.