Symmetry Group Cmm

Symmetry Group Cmm, a.k.a., C2mm for us nerds. This is a tessellation built within a 30 / 60 / 90 degree triangle. It has mirrors on the 2 short sides and a two-fold rotation on the hypotenuse.

The image below, with the highlighted triangle shows that the complete image is located within the unit cell of the triangle. A minimum of 3 lines needs to be drawn within, from point to point, the third one linking to the rotation point (red dot) in the middle of the hypotenuse.

Group-cmm-Batman-and-the-Bat - © 2013 Champagne Design

Group-cmm-Batman-and-the-Bat – © 2013 Champagne Design


The triangle pattern is not as obvious when you zoom-out from the image. The repeating element looks like a rectangle in this case.

Group-cmm-Batman-and-the-Bat (zoom out) — © 2013 Champagne Design

Group-cmm-Batman-and-the-Bat (zoom out) — © 2013 Champagne Design

Another example from a few months ago, when it was slightly colder outside!
You’ll have to tilt your head to see the Inuit. Snuggles.

Symmetry Group Cmm-The-Explorer-and-the-Inuit- © 2013 Champagne Design

Symmetry Group Cmm-The-Explorer-and-the-Inuit- © 2013 Champagne Design

And the same image, zoomed-out. No triangles apparent here either.

Group Cmm-The-Explorer-and-the-Inuit — © 2013 Champagne Design

Group Cmm-The-Explorer-and-the-Inuit — © 2013 Champagne Design

In trying to tell you how all of this is accomplished, with rotations, translations, mirrors and glides, within repeating shapes, I’m finding that it is more exhausting on my brain than actually doing the sketch! The drawing part is easy with the right tools. Either a traditional cardboard cutout or software.

An iPad app is available, which is what I have used here to create these images: KaleidoPaint by Jeff Weeks. Check it out.


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.

One thought on “Symmetry Group Cmm

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

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