Symmetry Group P4m

This tessellation method uses 3 reflections in a 45/45/90 degree triangle.  Fairly rigid looking tessellation as the 3 mirrors are quite apparent, and, on a zoom-out, the whole texture feels like a tartan cloth. To accomplish this tessellation, draw from the 3 points in the triangle to an arbitrary hook-up point somewhere inside the triangle, not necessarily the centre. No straying  over the mirror line is allowed though. You end up with 3 different outlines, all with bilateral symmetry. Quite similar to the previous post on symmetry group P3m1, but the angles are different here, 45/45/90 in this case.

The image below explains how three lines, from each of the triangle’s points, joined somewhere in the main area of the triangle, will create a tessellation in the P4m group. The red, the blue and the green lines joining at the yellow dot. The black lines are the mirrors. Flip the line in the mirror, each of the mirrors and repeat… ad evitam eternam. Then, just like imagining the Man in the Moon, draw a figure inside each of the three shapes.

Symmetry Group P4m-explained

Symmetry Group P4m-explained

Below, is one such design, zoomed-out… looks like a tartan cloth, or a tablecloth on the picnic table.

Symmetry-Group-p4m-zoomed-out

Symmetry-Group-p4m-zoomed-out

The image below was accomplished using P4m symmetry group, three lines create the outline of all 3 shapes, joining at the two hands and the edge of the black cape. All three figures have bilateral symmetry. Including the Peace sign on his t shirt.

Symmetry-Group-P4m-Prissy-Groovy-Cool- © 2013-Champagne-Design

Symmetry-Group-P4m-Prissy-Groovy-Cool- © 2013-Champagne-Design

Oxymora below is still another P4m tessellation.The Happy Buddhist, the Rasta Office Clerk, and the Fit Senior. The Buddhist’s fingertips, the Rasta Dude’s shoulder and the Senior’s elbow, is the point at which the three divider lines join.

Symmetry-Group-P4m-Oxymora-2013 © Champagne-Design

Symmetry-Group-P4m-Oxymora-2013 © Champagne-Design

That’s it for now, till the next symmetry group. A few more to go.

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.

10 thoughts on “Symmetry Group P4m

  1. Pingback: Symmetry Group P4m | champagnedesign

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  6. Pingback: P31m vs. P3m1 | champagnedesign

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  10. Pingback: Tessellations with KaleidoPaint | champagnedesign

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