Symmetry Group P6

This tessellation is laid out around a matrix of hexagons, a honeycomb. There is one 6 point rotation, one 3 point rotation and one 2 point rotation. Wicked to try to get a figure to fit in there and not look like something out of a fisheye lens! Definite exaggerations and stretched reality required. Never thought it would become one of my favourite systems.

Though complex in the number of rotation points, this type of tessellation is quite easy to accomplish. Locate the 3 different rotation points, one three-fold, one two-fold and one six-fold. The diagram below has them labelled as A, B and C. You have two lines to draw. Rambling over the hexagon’s outline, back and forth is permitted, as there are no mirrors. The first line connects point A to point B, both of these on the hexagon’s outline. The second line connects anywhere on that first line to the middle six-fold rotation point.

Symmetry Group P6 explained

Symmetry Group P6 explained

The above two simple lines, connecting A to B to C, were used as the base for the following tessellation. A cute pooper wearing a purple bandana with pink polka dots. Follow the black outline in both pictures, they are identical. Your tessellation can be complex, or quite simple, depends on your drawing style. In my case, I’ve been influenced by “la bande dessinée francophone”, since my youth. It has to be simple and humorous.

Symmetry Group p6 -Poopers with pink polka-dot on purple bandanas © 2013 Champagne Design

Symmetry Group p6 -Poopers with pink polka-dot on purple bandanas © 2013 Champagne Design

Zoomed-out, the hexagons become quite apparent.

Symmetry Group p6 -Poopers zoomed-out

Symmetry Group p6 -Poopers zoomed-out

Heel to Heel and Eye to Eye shows the type of exaggeration that may be required to fill this type of space. What’s really neat about this one is that the face is shared 3 ways! Reminds me of a webmaster I once knew out east. If you really want to get picky about tessellations, you can go the Ancient Egyptian style, where all body parts must be visible,accountable, accurate… But where’s the fun in that!

Symmetry Group P6 — Heel to Heel and Eye to Eye — © 2013 Champagne Design

Symmetry Group P6 — Heel to Heel and Eye to Eye — © 2013 Champagne Design

I’ve has a lot of fun with this symmetry group, now that I understand how it works. I have many more, but cannot include them all here. See if you can locate all three different rotation points in the images above and below.

Symmetry Group P6 — Where's the Litter Box — © 2013 Champagne Design

Symmetry Group P6 — Where’s the Litter Box — © 2013 Champagne Design

This one would be good for a T-shirt. I hesitated calling it “Mmmmm Sushi”, but instead came up with “10km Salmon Run”. On the same topic, the sockeye salmon run this year is at an all time, 30 year low. Must be all those harbour seals. No smoked salmon this year, unfortunately. We’ll have to smoke something else.

Symmetry Group P6 — 10Km Salmon Run — © 2013 Champagne Design

Symmetry Group P6 — 10Km Salmon Run — © 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.

Or a pair of scissors and a piece of cardboard works quite well. That’s how I learned.

Comments are always welcome!

One thought on “Symmetry Group P6

  1. Pingback: Symmetry Group P6 | champagnedesign

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