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!

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