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!
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


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

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.