The wizzle Geo 8 has been designed using the famous Koch (Koch snowflake) technique, which is one of the first fractals ever described. The Koch curve was published in 1904 by the Swedish mathematician Helge von Koch in a paper titled "On a Continuous Curve Without Tangents, Constructible from Elementary Geometry".

Geo 8 belongs to the p6 group of the  17 wallpaper symmetry groups, which has  centers of 6-fold rotation (60°) and distinct centers of 3-fold (120°) and 2-fold (180°) rotation (Baloglou, 2007). Geo 8 creates a periodic tessellation based on a triangular grid and possesses 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 Geo 8, you can observe the centers of 6-fold rotation in one of the three nodes of the initial 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".

For educational purposes, and not only, it is possible to create with the tiles of Geo 8 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), in order to be incorporated into educational projects and activities related to symmetries or containing geometric problems that implement various types of symmetries. You can find more details in the  "Wizzle in education".

Δείτε τη λύση του wizzle.