Symmetry Group P3m1

Images formed in a 3 mirrored equilateral triangle kaleidoscopic shape. Here as well, bilateral symmetry is at play. Three figures reflected in their 3 different mirrors, all 3 lines joining in the middle of the triangle, at an arbitrary location, not necessarily in the mid-point. See the diagram below. Mirror A, has a red line connecting both extremities. Mirror B, the blue line connects the same way, and needs to share its outline with the existing red line. The remaining area is basically the C mirror’s shape, by default. These are the two original lines that need the most tweaking when determining what type of creature you will eventually draw within.

Symmetry Group P3m1 explained

Symmetry Group P3m1 explained

Below is a quick elaboration on the above lines. The Wimp vs. Batman, with a torch filling the remaining area. I’ve highlighted the two main lines that create the tessellation. The red line reflected in one mirror creates the face by joining the two extremities of the mirror. The second mirror, has the black line from one edge of the mirror to the other, but sharing part of the way with the red line. They connect at the bottom tip of the ear. The third mirror has its shape determined by default. Cool symmetry rule to play with.

Symmetry-group-p3m1-explained - © 2013 Champagne Design

Symmetry-group-p3m1-explained – © 2013 Champagne Design

On zoom-out, an interesting mesh of barely visible triangles, in this case, because of the curved shapes within, it ends up looking like interlocking circles. Hexagons and Louis Cubes.



Here is one of my favourites, built with the P3m1 symmetry rule. The Elf, the Wizard and the Skeleton, where the 3 figures have a bit of topic fantasy in common. A bit more of a complex construction than the above drawing.

Symmetry Group P3m1 Elf-Wizard-Skeleton — © 2013 Champagne Design

Symmetry Group P3m1 Elf-Wizard-Skeleton — © 2013 Champagne Design

Or for something quick, try Louis Cubes, a favourite design of marquetry artists (the colouring is off according to them). Three simple straight lines, one from each point, joining in the middle of the equilateral triangle.

Symmetry Group P3m1 — Quick Louis Cubes — © 2013 Champagne Design

Symmetry Group P3m1 — Quick Louis Cubes — © 2013 Champagne Design

For a better illusion, the colours are corrected in Photoshop, below. All the tops are white, and shadows properly placed.

Symmetry-Group-P3m1 — Quick-Louis-Cubes-II — © 2013-Champagne-Design

Symmetry-Group-P3m1 — Quick-Louis-Cubes-II — © 2013-Champagne-Design

Here is another drawing built with P3m1 symmetry: The Bodybuilder, the Nerd, and the  Hugger aka, TATTARRATTAT. One long palindrome.

Symmetry Group p3m1 — TattarrattaT — © 2013 Champagne Design

Symmetry Group p3m1 — TattarrattaT — © 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
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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 P3m1

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