Symmetry Group Cmm

Symmetry Group Cmm, a.k.a., C2mm for us nerds. This is a tessellation built within a 30 / 60 / 90 degree triangle. It has mirrors on the 2 short sides and a two-fold rotation on the hypotenuse.

The image below, with the highlighted triangle shows that the complete image is located within the unit cell of the triangle. A minimum of 3 lines needs to be drawn within, from point to point, the third one linking to the rotation point (red dot) in the middle of the hypotenuse.

Group-cmm-Batman-and-the-Bat - © 2013 Champagne Design

Group-cmm-Batman-and-the-Bat – © 2013 Champagne Design

 

The triangle pattern is not as obvious when you zoom-out from the image. The repeating element looks like a rectangle in this case.

Group-cmm-Batman-and-the-Bat (zoom out) — © 2013 Champagne Design

Group-cmm-Batman-and-the-Bat (zoom out) — © 2013 Champagne Design

Another example from a few months ago, when it was slightly colder outside!
You’ll have to tilt your head to see the Inuit. Snuggles.

Symmetry Group Cmm-The-Explorer-and-the-Inuit- © 2013 Champagne Design

Symmetry Group Cmm-The-Explorer-and-the-Inuit- © 2013 Champagne Design

And the same image, zoomed-out. No triangles apparent here either.

Group Cmm-The-Explorer-and-the-Inuit — © 2013 Champagne Design

Group Cmm-The-Explorer-and-the-Inuit — © 2013 Champagne Design

In trying to tell you how all of this is accomplished, with rotations, translations, mirrors and glides, within repeating shapes, I’m finding that it is more exhausting on my brain than actually doing the sketch! The drawing part is easy with the right tools. Either a traditional cardboard cutout or software.

An iPad app is available, which is what I have used here to create these images: KaleidoPaint by Jeff Weeks. Check it out.

Capture

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.

Or this 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!

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