# Symmetry Group Pg — For all Soccer Fans

This symmetry group uses two parallel glide reflections. The glides can be either vertical or horizontal. In the image below, M.C. Escher has used vertical glides, which I’ve drawn-up for you, the black lines. Two alternating parallel lines, one at the rider’s heel, one through the horse’s rear hoof. The central block can be used as a stamp, it contains all the elements of the image, twice, one rider facing left, the same one facing right, one has been coloured with a different shade, for comprehension of the image.

M.C. Escher’s Knights tessellation with two alternating parallel glide lines

The image below, The Ultimate Soccer Dive, uses horizontal glide reflections. Guess I could have put the German colours on his jersey instead of Italy’s colours (sorry Jeff). But the latins do it so well, with so much emotion. The Argentinian, Maradona, popularized the now worldwide move decades ago. Diego does it well. So does Robben. And Muller. They’ve picked-up bad habits.  They all dive, it’s depressing, messes up the whole game. Brits have a bit more dignity and restraint. But I still root for Schalke04. The Royal Blues.

The Ultimate Soccer Dive — Player pulls his own hair, looks back in tremendous agony (and to check if the ref is watching), and dives to force a foul. Sheesh.

I talked about the “triple whip” in a previous post, I guess this is the “double whip”. In the image below, “A” identifies the corners of a rectangle. The first line connects point “A” with another instance itself on the same glide line. That’s the red line. The second line, in blue, also connects “A”, with another instance of itself, but across the other glide line. If we look at the rectangle, we end up with two lines whipping out from the same corner, to two of the other 3 corners.

Symmetry Group PG explained as two different, alternating parallel glide reflections

Below, another Pg tessellation. Trying to run away from a life of “Office Work”. Help. Hilfe. A l’aide. Time to go walk the dogs.

Symmetry Group Pg, Run Awaaaaay! – ©2013 Champagne Design

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!

🙂

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 Pg — For all Soccer Fans”

1. Charles says:

Hello, I would like to use some images in my master’s thesis in mathematics that I am writing, would it be possible?

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• Tell me more about your thesis! Use the contact link and form on the website. I am interested.
Francine

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