Don’t ask me how the software works, or about the geometry recalculations it does. I just want to share how cool this widget is. And ever so simple. All you need is the translatable tile, or the equivalent of a rectangular stamp of your tessellation, as a PNG file. It does the rest of the calculations and 3D mapping for you. Saves it as a .PDF file for you to print on your local colour printer. Then all you do is cut it up, score it, fold it, and glue it together.
The above tessellations were done on a tablet, using the iOrnament app. It automatically exports the tile for you, placing it ready in your email software. How easy is that! The 3D mapping widget only works on a computer, in a browser window. The link: http://science-to-touch.com/iOrnament3D/ As it says on the page, simply drag and drop your “tile” and click the arrow to proceed. Not all the 17 symmetry groups work on 3D surfaces (called platonic solids), so it takes a bit of trial and error.
I’ve tested a few of these symmetry groups.
- Group P6m: the black/blue/pink “flower of life” design above, originally has 6 mirrors. Here it is remapped in this instance , around a 20 sided figure, an icosahedron, dropping one of the mirrors, but not losing the symmetry or changing the design at all.
- Group P6: The tan coloured Dachshund tessellation above, is originally built around a 6 point, a three point and a two point rotation. Here it has been remapped on a dodecahedron, built of 12 pentagons. The original 6 swirling tails are respun using only 5 tails!
- Group P4g: The Soccer Kid (#88) tessellation above has also been remapped to fit a hexahedron using different symmetry operations.
- Group P4: Blue and White Schalke Fan tessellation in the photo above was created using the following symmetry operations 2 four way rotations, and one two way rotation. It was printed on a cube, a.k.a. hexahedron. In the image below, the Whirling Dervish has been mapped onto an octahedron, an 8 sided shape built of triangles. I’ve also printed this Whirling Derouiche tessellation onto a dodecahedron, but have not yet cut and glued it.
Below, from the Wikipedia page, an image with the five platonic solids.
2017-05-04: A new App called “iO Crafter” on the iPad has just come out, from Jürgen Richter-Gebert. It performs the above function as well as others.
- build a platonic solid
- build a kaleidocycle
- view a kaleidoscope
- hyperbolic kaleidoscope
- map your art into a spiral deformation
- conformal maps