KaleidoTile

KaleidoTile is a software that allows you to learn about polyhedra and tilings while simultaneously creating beautiful and colorful kinematic art. With the flat style, you can create traditional polyhedra, but the curved style lets you smooth your polyhedra into tilings of the sphere, Euclidean plane or hyperbolic plane. It's versatile and provides a unique approach to learning about geometry.

Not only can you create your own art, but you can decorate your work with your own pictures or use the built-in pictures and color palettes. KaleidoTile has the capability of morphing any polyhedron or tiling into another within each symmetry group. For example, you can morph a dodecahedron to an icosahedron and confirm that they share the same symmetries.

Although KaleidoTile is intended mainly for grades 9-12, it has also been found useful in middle schools for introducing symmetry through art, and even in college geometry courses for studying symmetry groups. Extending the software's capabilities, it comes with a set of questions on Tilings and Symmetry for small group investigation. Overall, KaleidoTile is an educational and fun way to learn about geometry while creating beautiful art.