Geo 1 (L 1)
Difficulty degree:
1 2 3 4 5 6
Designer:
Dorothea Makroglou
The wizzle "Geo 1" is available in the basic version of 40 tiles in two colors (20 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 40 tiles: 8€
More maths
The wizzle Geo1 belongs to the pgg symmetry group of 17 wallpaper symmetry groups, which has glide-reflection in two perpendicular directions, but lacks reflection. It also has centers of 2-fold rotation (180°), but these are not on the glide reflection axes (Baloglou, 2007).
Geo1 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 Geo1, you can discern the centers of 2-fold rotation in the nodes of the initial square grid and in between them the axes of glide-reflection. These isometries also constitute the elementary solving rule of Geo1. A set of four tiles forms the basic structural unit of the infinitely repeating (with the translation isometry) pattern that fills the Euclidean plane, providing a second approach to solving Geo1.
For educational purposes, and not only, you can use the tiles of the Geo 1 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".