Deciding which symmetry group to use for a specific design can be hit and miss. And try again. You can narrow it down by establishing if your design needs bilateral symmetry. This would eliminate 7 mirrorless groups out of a possible 17. Or whether you want rotations. Glides add a flowing movement to the design. Your choice. Have a look at the table below, it may help guide your efforts.
2016-10-31 : I have since created a new “Cheat Sheet” of my own. Please read “Symmetry group thumbnails and listing systems“.
A challenge would be to complete a Hummingbird tessellation in all 17 symmetry groups. I’m more than halfway there. A hummingbird series has been created in the following symmetry groups: P4g, P6 (2 of those), Cm, P2, Pmm, P3m1, P4m, Pg, and Cm. Some are sketches that will probably never be completed. Some of them are superb colourful, flowing designs. Send me your hummer and I’ll post it here!
Lots of software out there to help you accomplish this type of design.
An iPad app is available, which is what I have used here to create these images: KaleidoPaint by Jeff Weeks.
There is also a java-based program “Escher Web Sketch” at the Ecole Polytechnique de Lausanne. Make sure Java is enabled and not blocked by your security software.
Also, another screen-based software by Anselm Levskaya Escher Sketch v2.
Or a pair of scissors and a piece of cardboard works quite well. That’s how I learned.
Comments are always welcome!