The wizzle El Drago belongs to the p3 symmetry group of the 17 wallpaper symmetry groups, which only has 3-fold rotation (120°) (Baloglou, 2007). El Drago 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 the El Drago, you can observe the distinct centers of 3-fold rotation in the three out of the six nodes of the hexagonal grid. This isometry also constitutes the elementary solving rule of the El Drago. A set of three tiles (assembled in three different ways, meaning around the three distinct 3-fold rotation centers)  form a meta-tile, the basic structural unit of the infinitely repeating (with translation isometry) pattern that fills the Euclidean plane, providing a second approach to solving the El Drago.

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.