The wizzle  Hippofox belongs to the  p4 symmetry group of the 17 wallpaper symmetry groups, which has centers of 4-fold rotation (90°) and distinct centers of 2-fold rotation (180°) (Baloglou, 2007). The Hippofox 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 Hippofox, you can observe the isometries of the distinct centers of 4-fold and 2-fold rotation in the nodes of the square grid. These isometries also constitute the elementary solving rule of the Hippofox. 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 Hippofox.

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