Symmetry Group P3

Symmetry group P3, or 3 rotations through 120 degrees. This is quite a versatile symmetry group, and easy to accomplish. Only two lines to draw the outline of your classic tessellation. Basically, you draw any line through the edge of a hexagon, linking two of the three-way rotation points, and you will get a closed shape after 3 fold rotation. That last rotation point will need to link with the first line. Three different 120 degree rotation points around a hexagon. See the technical drawing below.



Three rotation points, A, B and C. The first line, red,  links A to C. Any wiggly line will do and straying from the area is permitted, encouraged. The second line links point B, to anywhere on the first line. This will give you a single, repeating shape, showing up 3 times in the hexagon, shown here as the fine grey line. Now all you have to figure out is what to fit inside! The possibilities are endless and fun.

The Jewel Thief below, was created using this symmetry rule.

Symmetry-Group-p3-Jewel-Thief - © 2013 Champagne Design

Symmetry-Group-p3-Jewel-Thief – © 2013 Champagne Design

Zoomed-out, the hexagon becomes quite apparent.



Below is another P3 symmetry drawing that I’ve name “Rabid Rabbit”. Zoomed-out. The hexagons are quite visible in this one. Not quite as visible when you zoom-in.



Wicked rabbits. Garden munchers.

Symmetry-Group-P3-Rabid-Rabbit - © 2013 Champagne Design

Symmetry-Group-P3-Rabid-Rabbit – © 2013 Champagne Design

Get out there and try it!

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.

Or this 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!

If you’re a “Learn by Seeing” “Learn by Doing” kind of person, I’ve started creating videos on “how-to” create tessellations. I’ll be covering each of the 17 symmetry groups, one class at a time. And like all artists, we need to make a living. So. I’ve uploaded these to the Skillshare platform. I’ll get paid by minutes watched.

You can take the classes for free. Skillshare offers anywhere from 2 weeks to a month for free if you sign up, even temporarily.

You can register for just a month and cancel anytime. It’s less than the cost of a Netflix subscription!
There are over 40,000 classes on topics for creative persons just like you. Join my mailing list, either here on my blog (in the sidebar), or a at this link for a specific list I use to announce new classes.

I’d love for you to join me on this wonderful learning adventure.

If you prefer, you can follow my progress on social media, I always announce my new class:
Facebook: Franc Champagne, and Vancouver Island Tessellation Artist
Instagram: champagne.francine
Twitter: FChampagne1
Linkedin: Graphic Design, PowerPoint and tessellations
Youtube: Video animations and class intros

3 thoughts on “Symmetry Group P3

  1. Pingback: Dash Hound tessellation | Tessellations, images in regular division of the plane

  2. Pingback: Re-Creating M.C. Escher’s Lizard #Tessellation | Tessellations, images in regular division of the plane

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