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! And you can still stay put on the couch. 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

My classes have received an independent rating of 9.7/10, placing these Skillshare classes in the TOP 2% of classes reviewed by CourseMarks!


Rekindle your Love of M.C. Escher Tessellations, draw your own tessellations using a free iPad App rating

Here is a list of the classes up so far:

  1. Rekindle your Love of M.C. Escher Tessellations, draw your own tessellations using a free iPad App. In this class I introduce the concept of tessellations, show you the work of M.C. Escher as well as other artists. Then we dive into a first symmetry method, P4g, accomplished by drawing only one line to create the perimeter of your tessellation.
  2. Just like M. C. Escher’s Tessellations: Draw Using a New Symmetry Method and Your iPad. We tackle the Mirrored Triplets symmetry group, aka P3m1.
  3. This UP/DOWN, LEFT/RIGHT Tessellation method was M. C. Escher’s favorite. It is also the symmetry method, P1, most taught in schools. Probably the only way most artists have tried to accomplish a nested shape. We will push it a tad farther, but also easier than scissors and cardboard.
  4. M. C. Escher Tessellations: The Three Cozy Buddies Symmetry Group, know as symmetry group P3. Lots of examples, from many different tessellation artists. One of my favorite ways of creating tessellations.
  5. Digital Patterns: Super Simple Quickie Patterns. 20 patterns in 30 minutes! I will show you how to draw and assemble your pattern design elements in four different and unusual ways. Come explore the possibilities, from a different point of view using your iPad and the free KaleidoPaint app. There is more to symmetry than rigid repeats, half-drops and tossed layouts.
  6. My next class with deal with a symmetry group I have named: “This way — that way”, aka crystallographic notation Pg. That Koloman Moser video above, is part of the series.

4 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

  3. Pingback: KaleidoPaint iPad App Help | Tessellations by Francine Champagne

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.