The wizzle Pegasus belongs to the pg symmetry group of the 17 wallpaper symmetry groups, which has glide-reflection in one direction but lacks reflection (Baloglou, 2007). The Pegasus creates a periodic tessellation based on a square 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 Pegasus, you can observe the isometries of horizontal translation and vertical glide-reflection. These isometries also constitute the elementary solving rule of the Pegasus. A set of four 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 the Pegasus.

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