Geo 4
Difficulty degree:
1 2 3 4 5 6
Designer:
Korina Xanthopoulou
The wizzle "Geo 4" is available in the basic version of 42 tiles in three colors (14 tiles of each color), as well as in the extednded edition of 57 tiles (19 tiles of each color) and you can choose from a variety of color combinations. We can create personalized versions for you with the number of tiles and color combination you desire. Here are the available colors and possible combinations.
Check out the "How to Play" section to see how to use the wizzle and discover many ways you can make use of it. You can also suggest your own ideas for what you can do with the wizzle, which, if you wish, we will share in the "Creativity & Learning Community" section to make them accessible to the entire wizzle user community.
Cost of the basic version of 42 tiles: 9€ Cost of the basic version of 57 tiles: 12€
More maths
The Geo 4 wizzle belongs to the p3 symmetry group of the 17 wallpaper symmetry groups, which only has the isometry of 3-fold rotation (120°) (Baloglou, 2007). Geo 4 creates a periodic tessellation based on a hexagonal grid and has the trivial isometry of 360° as well as many trivial isometries of translation (horizontal, vertical, diagonal). In the above images, where you see the tessellation created by Geo 4, you can observe the centers of 3-fold rotation at three of the six nodes of the initial hexagonal grid. The isometry of 3-fold rotation also constitutes the elementary solution rule for Geo 4. A set of 3 tiles assembled in three different ways, i.e., around the three different centers of 3-fold rotation, forms a metatile, the basic structural unit of the infinitely repeating (with translation isometry) pattern that fills the Euclidean plane, providing a second approach to solving Geo 4.
For educational purposes, it is possible to generate with Geo 4 tiles of all kinds of symmetries (translation, reflection, glide reflection, all types of rotations, 2-fold, 3-fold, 4-fold, 6-fold,... and compositions of symmetries). These can be incorporated into educational projects and activities related to symmetries or containing geometric problems that implement various types of symmetries in their shapes. You can find more details in the section "Wizzle in education".