Symmetry Group P4g

My first ever tessellation was accomplished using this P4g symmetry group.

My understanding occurred during a class on crystallography, works with the same principles. What a blast that was. Hooked since then.

The basic concept is a 4-way rotation inside a square, built of mirrors. One line from the rotation point to the perimeter corner will give you four halves of an identical figure.

First ever tessellation sketch using symmetry group p4g

First ever tessellation sketch using symmetry group p4g

If two lines are drawn from the rotation point, to anywhere on the perimeter, two figures will appear, such as in MCE’s Angels and Devils, below.

MC Escher's Angels and Demons, are built using symmetry group P4g

MC Escher’s Angels and Demons, are built using symmetry group P4g

Quick identification method for symmetry group P4g:

1- mirror symmetry down the body,

2- figures are head to head and feet to feet, hooked at the arms/elbows/hands/wings…

3- 90 degree rotations at the arms… always end up looking the same, in my case anyhow

Symmetry Group P4g, Look Ma, I Have Two Watches

Symmetry Group P4g, Look Ma, I Have Two Watches

P4g used to be my favourite symmetry group, before software came out. I’ve since expanded my repertoire and now prefer the total absence of mirrors in designs — really enjoying P6 and P3.

The image below illustrates the two lines to the perimeter concept, Two Fitness Styles, one dude posing his bodybuilding skills, the other doing his yoga thing. Note the area sharing for the heads! I seem to be doing a lot of that.

Symmetry Group P4g, Two Fitness Styles

Symmetry Group P4g, Two Fitness Styles

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.

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.

3 thoughts on “Symmetry Group P4g

  1. Pingback: Symmetry Group P4g | champagnedesign

  2. Pingback: One line, one fill, tessellation | My tessellations, images in regular division of the plane

  3. Pingback: Puppy Training tessellation | My tessellations, images in regular division of the plane

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