Symmetry Group Pgg

This symmetry group is one of my favourites, as it uses glides as well as rotations in its construction. No mirrors here, so the tessellated figures do not need to be bilaterally symmetric constructs. Glides are one more trick to tickle your visual perception.

Accomplishing the division of the surface using this symmetry method consists in linking one of the two-fold rotation points (R1) to one of the corners (red line 1) From that same corner, draw a line to the other adjacent corner (green line 2).  Only one two-fold rotation point is left (R2). Connect R2 to anywhere, using any curve. Now stare at it till your eyes cross (just kidding) and you might see a figure emerge. Imagination. Try it. Delete it. Try again till you can edit the line to form a figure.

Symmetry Group Pgg explained

Symmetry Group Pgg explained

Dad was an Usher for a summer job, when he was a youngster. A Posh Usher, uniform and all. Cool job, because you get to see all the movies. Over and over… well maybe not. The green dots and red dots indicate the two different 180 degree rotation points, same as R1 and R2 in the above. The dashed line indicates the glide-reflection line, which can be viewed as moving the figure in translation with at the same time a mirror applied to it.

Symmetry Group Pgg — The Posh Usher — © 2013 Champagne Design

Symmetry Group Pgg — The Posh Usher — © 2013 Champagne Design

The sketch below uses the same symmetry group; Involuntary Suicide… where the guy has the barrel of his weapon in the other guy’s mouth, which happens to be himself! Can you locate the two rotation points?

Symmetry Group Pgg — Involuntary Suicide — © 2013 Champagne Design

Symmetry Group Pgg — Involuntary Suicide — © 2013 Champagne Design

One rotation point at the tip of his t shirt at the belly, the other rotation point at his calf, right or left depending which clone you’re looking at.

Lots of software out there to help you accomplish this type of design.

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.

Also, another screen-based software by Anselm Levskaya Escher Sketch v2. (I used to have a basic Mac-based software, way back in prehistory, 1995, by the same name. It worked on the cutesy first Mac)

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 Pgg

  1. Pingback: Mouse tessellation ~ Symétruc de souris | Tessellations, images in regular division of the plane

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