The wizzle Sokratosaurus belongs to the p6 symmetry group of the 17 wallpaper symmetry groups which has center of 6-fold rotation (60°), centers of 3-fold rotation (120°) and centers of 2-fold rotation (180°) (Baloglou, 2007). The Sokratosaurus creates a periodic tessellation based on a triangular grid, thus possesing 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 Sokratosaurus, you can observe the centers of 6-fold rotation in one of the three nodes of the main triangular grid and the centers of 3-fold rotation in the other two nodes. The 2-fold rotation centers are found in the middle of the segments that connect the 3-fold rotation centers.  These isometries constitute the elementary solving rule of the Sokratosaurus. A set of six tiles around the center of the 6-fold rotation forms 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 Sokratosaurus.

For educational purposes, and not only, you can use the tiles of the Sokratosaurus 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 οn the plane. You can find more details in the section "Wizzle in education".

Δείτε τη λύση του wizzle.