Group Pmm is also known as P2mm in Peter S. Stevens’ Handbook of Regular Patterns. A four-sided mirrored box. Figures with bilateral symmetry work best in this type of group.
One for each mirror is a possibility. A line drawn from each mirror corner to its twin will delineate the four figures into a tessellation.
The image below shows a Pmm symmetry group tessellation, fully zoomed-out. The rectangular structure is quite apparent. Of course, the trick is to turn all of this into a recognizable object!
This is the same tessellation, zoomed-in. It shows the unit cell, the rectangle, with its four mirrors.
Mosquito / Moth / Beaver / Boy is another example of this Pmm symmetry group.
Have fun with the KaleidoPaint iPad app. I will attempt to illustrate all 17 ways you can divide a two dimensional surface with this cool app, from the billions of possible drawings.
If you don’t have an iPad, you can try the Java-based program “Escher Web Sketch” at the Ecole Polytechnique de Lausanne. It works just as well to create your shapes.
Or this screen-based software by Anselm Levskaya Escher Sketch v2.
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
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!
Here is a list of the classes up so far:
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.