Chanced upon Keith Enevoldsen’s chart of symmetries a few months back. I find it very well illustrated to show all 17 plane symmetry groups. With his permission, I have reproduced it here.
What is useful here, other than plane groups, is that he has also included Point Group symmetries, as well as Line Group symmetries.
Point groups are used by many artists and popular these past few years by mandala artists. They use any number of divisions, and very often these are mirrors.
Line groups can be used for friezes, bands, and by ribbon artists. Point and line groups are a good place to start if you want to learn to create nested shapes. That’s where I got my start. Many decades ago.
I have written a few posts on this symmetry chart topic. Here is a list of those previous Plane Groups posts:
Which symmetry group to use? In this blog post I show that you can use many different symmetry groups to accommodate your chosen topic. Not all the results end up aesthetically pleasing — it is a good exercise in stretching your imagination. In this post, I’ve used a favourite topic of mine, hummingbirds.
Symmetry group thumbnails and listing systems is my own cheat sheet for plane symmetry. I’ve used hand icons as the illustrating unit, as I keep on using my own hands when talking about symmetry. Below this cheat sheet, I’ve placed more details in a table, which lists the Orbifold Notation, Wallpaper Group, and the system I’ve used for decades, the Hermann Mauguin Symbols. The last column in the table you will find a very special paragraph explaining the trick required to draw a nested shape.
Create a Nested Shape #Tessellation in any Symmetry Group list all the 17 links to my technical shortcuts, in all 17 plane symmetry groups.
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Check out other tessellation artists around the globe!
David bailey in the UK has an exhaustive list of tessellation artists, much work has been put into his research. Thanks David.
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